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USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to INTERPRETING CONFIDENCE INTERVALS Some points to consider: 95 % confidence is a confidence that in the long-run 95 % of the CIs will include the population mean. It is a confidence in the algorithm and not a statement about a single CI. In frequentist terms the CI either contains the population mean or it does not. It’s just one from the dance of CIs to cite Geoff Cumming. WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values for UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to INTERPRETING CONFIDENCE INTERVALS Some points to consider: 95 % confidence is a confidence that in the long-run 95 % of the CIs will include the population mean. It is a confidence in the algorithm and not a statement about a single CI. In frequentist terms the CI either contains the population mean or it does not. It’s just one from the dance of CIs to cite Geoff Cumming. WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
VISUALIZATIONS
Posters. I used to sell posters on Etsy, but after making 95 sales (a magic number in science) I decided to stop and share the digital files here for free instead.You can print them in whatever way that fits you. If you want to support me just Buy Me a Coffee or share this page, or print the posters using this affiliate link Printful print-on-demand (it's the company I used when I sold these UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING P-VALUES A tool to understand p-values using an interactive simulation. the world can never have enough of these beautiful, simple, easily-understood visualizations of basic stats concepts stats is hard for many. i also used to find stats hard. so here's another tools to add to our repertoire, to help build our students' intuitiveunderstanding.
UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values for MONTY HALL SIMULATIONS The Monty Hall Problem. There’ve been many simulations of the Monty Hall-problem done in R. But since I’m trying to learn R, I wanted to try to simulate the paradox over many different trails and plot them all using ggplot2.The problem was originally posed as follows (fromwikipedia):
INTERPRÉTER LE D DE COHEN Avec un d de Cohen de 0.8, 78.8% du groupe "treatment" a une valeur supérieure à la moyenne du groupe "control" (U 3 de Cohen), 68.9% des deux groupes se chevauchent, et il y a 71.4% de chances qu'une personne choisie au hasard dans le groupe traitement ait un score plus élevé qu'une personne choisie au hasard dans le groupe contrôle (probabilité de supériorité). POWER ANALYSIS FOR LONGITUDINAL MULTILEVEL MODELS Thank you for making such useful and pretty tools. It not only helped me understand more about power, effect size, etc, but also made my quanti-method class more engaging and interesting. NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes. HETEROGENEOUS TREATMENT EFFECTS AND HOMOGENEOUS OUTCOME Recently there has been a couple of meta-analyses investigating heterogeneous treatment effects by analyzing the ratio of the outcome variances in the treatment and control group. The argument made in these articles is that if individuals differ in their response, then observed variances in the treatment and control group in RCTs shoulddiffer.
TOLK COHENS D
Med en Cohens d på 0.8, kommer 78.8% av "treatment"-gruppa å være over gjennomsnittsverdien for "control"-gruppa (Cohens U 3), 68.9% av de to gruppene til å være overlappende, og det er en 71.4% sjanse å tilfeldig utvalgt person fra "control"-gruppa kommer ha en høyere poengscore enn en tilfeldig utvalgt person fra "treatment"-gruppa (probability of superiority). START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values for UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to INTERPRETING CONFIDENCE INTERVALS Some points to consider: 95 % confidence is a confidence that in the long-run 95 % of the CIs will include the population mean. It is a confidence in the algorithm and not a statement about a single CI. In frequentist terms the CI either contains the population mean or it does not. It’s just one from the dance of CIs to cite Geoff Cumming. WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values for UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to INTERPRETING CONFIDENCE INTERVALS Some points to consider: 95 % confidence is a confidence that in the long-run 95 % of the CIs will include the population mean. It is a confidence in the algorithm and not a statement about a single CI. In frequentist terms the CI either contains the population mean or it does not. It’s just one from the dance of CIs to cite Geoff Cumming. WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
VISUALIZATIONS
Posters. I used to sell posters on Etsy, but after making 95 sales (a magic number in science) I decided to stop and share the digital files here for free instead.You can print them in whatever way that fits you. If you want to support me just Buy Me a Coffee or share this page, or print the posters using this affiliate link Printful print-on-demand (it's the company I used when I sold these UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING P-VALUES A tool to understand p-values using an interactive simulation. the world can never have enough of these beautiful, simple, easily-understood visualizations of basic stats concepts stats is hard for many. i also used to find stats hard. so here's another tools to add to our repertoire, to help build our students' intuitiveunderstanding.
UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values for MONTY HALL SIMULATIONS The Monty Hall Problem. There’ve been many simulations of the Monty Hall-problem done in R. But since I’m trying to learn R, I wanted to try to simulate the paradox over many different trails and plot them all using ggplot2.The problem was originally posed as follows (fromwikipedia):
INTERPRÉTER LE D DE COHEN Avec un d de Cohen de 0.8, 78.8% du groupe "treatment" a une valeur supérieure à la moyenne du groupe "control" (U 3 de Cohen), 68.9% des deux groupes se chevauchent, et il y a 71.4% de chances qu'une personne choisie au hasard dans le groupe traitement ait un score plus élevé qu'une personne choisie au hasard dans le groupe contrôle (probabilité de supériorité). POWER ANALYSIS FOR LONGITUDINAL MULTILEVEL MODELS Thank you for making such useful and pretty tools. It not only helped me understand more about power, effect size, etc, but also made my quanti-method class more engaging and interesting. NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes. HETEROGENEOUS TREATMENT EFFECTS AND HOMOGENEOUS OUTCOME Recently there has been a couple of meta-analyses investigating heterogeneous treatment effects by analyzing the ratio of the outcome variances in the treatment and control group. The argument made in these articles is that if individuals differ in their response, then observed variances in the treatment and control group in RCTs shoulddiffer.
TOLK COHENS D
Med en Cohens d på 0.8, kommer 78.8% av "treatment"-gruppa å være over gjennomsnittsverdien for "control"-gruppa (Cohens U 3), 68.9% av de to gruppene til å være overlappende, og det er en 71.4% sjanse å tilfeldig utvalgt person fra "control"-gruppa kommer ha en høyere poengscore enn en tilfeldig utvalgt person fra "treatment"-gruppa (probability of superiority). START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE Kristoffer Magnusson's blog. Thank you for making such useful and pretty tools. It not only helped me understand more about power, effect size, etc, but also made my quanti-method class more engagingand interesting.
VISUALIZATIONS
Posters. I used to sell posters on Etsy, but after making 95 sales (a magic number in science) I decided to stop and share the digital files here for free instead.You can print them in whatever way that fits you. If you want to support me just Buy Me a Coffee or share this page, or print the posters using this affiliate link Printful print-on-demand (it's the company I used when I sold these INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values for USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Support my work. The content on this blog is shared for free under a CC-BY license. If you like my work and want to support it you can: Buy me a coffee (or use PayPal). You can also sponsor my open source work using GitHub Sponsors WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes. START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE Kristoffer Magnusson's blog. Thank you for making such useful and pretty tools. It not only helped me understand more about power, effect size, etc, but also made my quanti-method class more engagingand interesting.
VISUALIZATIONS
Posters. I used to sell posters on Etsy, but after making 95 sales (a magic number in science) I decided to stop and share the digital files here for free instead.You can print them in whatever way that fits you. If you want to support me just Buy Me a Coffee or share this page, or print the posters using this affiliate link Printful print-on-demand (it's the company I used when I sold these INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values for USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Support my work. The content on this blog is shared for free under a CC-BY license. If you like my work and want to support it you can: Buy me a coffee (or use PayPal). You can also sponsor my open source work using GitHub Sponsors WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes.ABOUT KRISTOFFER
Questions. Please use GitHub Discussions for any questions related to this site, or open an issue on GitHub if you've found a bug or wan't to make a feature request.. Contact. You can get in contact with via hello rpsychologist.com or on Twitter @krstoffr, and feel free to add me on LinkedIn.. You can also come hang out and chat with me on the open science discord Git Gud Science.VISUALIZATIONS
Posters. I used to sell posters on Etsy, but after making 95 sales (a magic number in science) I decided to stop and share the digital files here for free instead.You can print them in whatever way that fits you. If you want to support me just Buy Me a Coffee or share this page, or print the posters using this affiliate link Printful print-on-demand (it's the company I used when I sold theseBLOG ARCHIVE
Kristoffer Magnusson's blog. Most content on this blog is licensed under a CC-BY or CC0 license, the specific license for each page willappear here.
UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values for UNDERSTANDING CORRELATIONS Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show UNDERSTANDING P-VALUES A tool to understand p-values using an interactive simulation. the world can never have enough of these beautiful, simple, easily-understood visualizations of basic stats concepts stats is hard for many. i also used to find stats hard. so here's another tools to add to our repertoire, to help build our students' intuitiveunderstanding.
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to INTERPRETING CONFIDENCE INTERVALS Donate. The content on this blog is shared for free under a CC-BY license. If you like my work and want to support it you can: Buy me a coffee (or use PayPal). You can DISTRIBUTION OF P-VALUES WHEN COMPARING TWO MEANS Limitations. This visualization is based on a two-sample Z-test, i.e. we assume that the true standard deviation is known.In real life this is often not the case, which is why t-tests are much more common. When the effect is nonzero p-values from t-tests follow a non-central t distribution. However, the formulas used here works quite well as normal approximation of the non-central t UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Support my work. The content on this blog is shared for free under a CC-BY license. If you like my work and want to support it you can: Buy me a coffee (or use PayPal). You can also sponsor my open source work using GitHub Sponsors START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Finding the Maximum Likelihood Estimates. Since we use a very simple model, there's a couple of ways to find the MLEs. If we repeat the above calculation for a wide range of parameter values, we get the plots below. The joint MLEs can be found at the top of contour plot, which shows the likelihood function for a grid of parameter values. UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes. START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Finding the Maximum Likelihood Estimates. Since we use a very simple model, there's a couple of ways to find the MLEs. If we repeat the above calculation for a wide range of parameter values, we get the plots below. The joint MLEs can be found at the top of contour plot, which shows the likelihood function for a grid of parameter values. UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes.ABOUT KRISTOFFER
About. I'm Kristoffer Magnusson a researcher in clinical psychology at the Centre for Psychiatry Research, Karolinska Institutet, in Stockholm, Sweden. My interests are a mix of open science, gambling problems, statistics, therapist effects, visualization, and psychotherapy. I also have a background in web development, and Istill dabble with
VISUALIZATIONS
Posters. I used to sell posters on Etsy, but after making 95 sales (a magic number in science) I decided to stop and share the digital files here for free instead.You can print them in whatever way that fits you. If you want to support me just Buy Me a Coffee or share this page, or print the posters using this affiliate link Printful print-on-demand (it's the company I used when I sold these UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values forBLOG ARCHIVE
Slides from my talk on how to do power analysis for longitudinal 2- and 3-level models. 2018-04-11. MONTY HALL SIMULATIONS The Monty Hall Problem. There’ve been many simulations of the Monty Hall-problem done in R. But since I’m trying to learn R, I wanted to try to simulate the paradox over many different trails and plot them all using ggplot2.The problem was originally posed as follows (fromwikipedia):
INTERPRETING CONFIDENCE INTERVALS Some points to consider: 95 % confidence is a confidence that in the long-run 95 % of the CIs will include the population mean. It is a confidence in the algorithm and not a statement about a single CI. In frequentist terms the CI either contains the population mean or it does not. It’s just one from the dance of CIs to cite Geoff Cumming. UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
DISTRIBUTION OF P-VALUES WHEN COMPARING TWO MEANS Limitations. This visualization is based on a two-sample Z-test, i.e. we assume that the true standard deviation is known.In real life this is often not the case, which is why t-tests are much more common. When the effect is nonzero p-values from t-tests follow a non-central t distribution. However, the formulas used here works quite well as normal approximation of the non-central t START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Finding the Maximum Likelihood Estimates. Since we use a very simple model, there's a couple of ways to find the MLEs. If we repeat the above calculation for a wide range of parameter values, we get the plots below. The joint MLEs can be found at the top of contour plot, which shows the likelihood function for a grid of parameter values. UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes. START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Finding the Maximum Likelihood Estimates. Since we use a very simple model, there's a couple of ways to find the MLEs. If we repeat the above calculation for a wide range of parameter values, we get the plots below. The joint MLEs can be found at the top of contour plot, which shows the likelihood function for a grid of parameter values. UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes.ABOUT KRISTOFFER
About. I'm Kristoffer Magnusson a researcher in clinical psychology at the Centre for Psychiatry Research, Karolinska Institutet, in Stockholm, Sweden. My interests are a mix of open science, gambling problems, statistics, therapist effects, visualization, and psychotherapy. I also have a background in web development, and Istill dabble with
VISUALIZATIONS
Posters. I used to sell posters on Etsy, but after making 95 sales (a magic number in science) I decided to stop and share the digital files here for free instead.You can print them in whatever way that fits you. If you want to support me just Buy Me a Coffee or share this page, or print the posters using this affiliate link Printful print-on-demand (it's the company I used when I sold these UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Before we do any calculations, we need some data. So, here's 10 random observations from a normal distribution with unknown mean (μ) and variance (σ²). Y = We also need to assume a model, we're gonna go with the model that we know generated this data: y ∼ N (μ, σ 2) y \sim \mathcal N(\mu, \sigma^2) y ∼ N (μ, σ 2).The challenge now is to find what combination of values forBLOG ARCHIVE
Slides from my talk on how to do power analysis for longitudinal 2- and 3-level models. 2018-04-11. MONTY HALL SIMULATIONS The Monty Hall Problem. There’ve been many simulations of the Monty Hall-problem done in R. But since I’m trying to learn R, I wanted to try to simulate the paradox over many different trails and plot them all using ggplot2.The problem was originally posed as follows (fromwikipedia):
INTERPRETING CONFIDENCE INTERVALS Some points to consider: 95 % confidence is a confidence that in the long-run 95 % of the CIs will include the population mean. It is a confidence in the algorithm and not a statement about a single CI. In frequentist terms the CI either contains the population mean or it does not. It’s just one from the dance of CIs to cite Geoff Cumming. UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
DISTRIBUTION OF P-VALUES WHEN COMPARING TWO MEANS Limitations. This visualization is based on a two-sample Z-test, i.e. we assume that the true standard deviation is known.In real life this is often not the case, which is why t-tests are much more common. When the effect is nonzero p-values from t-tests follow a non-central t distribution. However, the formulas used here works quite well as normal approximation of the non-central t START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
INTERPRETING CONFIDENCE INTERVALS Some points to consider: 95 % confidence is a confidence that in the long-run 95 % of the CIs will include the population mean. It is a confidence in the algorithm and not a statement about a single CI. In frequentist terms the CI either contains the population mean or it does not. It’s just one from the dance of CIs to cite Geoff Cumming. USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes. WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
START | R PSYCHOLOGISTINTERPRETING CONFIDENCE INTERVALSNEW PAPERCONFOUNDINGVISUALIZATIONSTREATMENT RESPONSE powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub. INTERPRETING COHEN'S D With a Cohen's d of 0.8, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U 3), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group (probability of superiority). ). Moreover, in order to have one more favorable UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then UNDERSTANDING EQUIVALENCE, NON-INFERIORITY AND SUPERIORITY Non-inferiority is shown if the lower side of a two-sided (1–2α)×100% CI is above -Δ. In this case that means a 95 % CI, so the significance level is 0.025. Using the two one-sided test (TOST) procedure, equivalence is tested using a (1–2α)×100% CI. In this case this significance level is also 0.025. In the visualizationsuperiority
INTERPRETING CONFIDENCE INTERVALS Some points to consider: 95 % confidence is a confidence that in the long-run 95 % of the CIs will include the population mean. It is a confidence in the algorithm and not a statement about a single CI. In frequentist terms the CI either contains the population mean or it does not. It’s just one from the dance of CIs to cite Geoff Cumming. USING R AND LME/LMER TO FIT DIFFERENT TWO- AND THREE-LEVEL Using R and lme/lmer to fit different two- and three-level longitudinal models. I often get asked how to fit different multilevel models (or individual growth models, hierarchical linear models or linear mixed-models, etc.) in R. In this guide I have compiled some of the more common and/or useful models (at least common in clinicalpsychology
UNDERSTANDING STATISTICAL POWER AND SIGNIFICANCE TESTING Tweet; Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has been said about significance testing – most of it negative. Methodologists constantly point out that researchers misinterpret p-values.Some say that it is at best a meaningless exercise and at worst an impediment to NEW D3.JS VISUALIZATION: THE T-DISTRIBUTION AND ITS NORMAL I just published a new interactive visualization in my series of basic statistical concepts and techniques. This time I am trying to show how the t-distribution and the normal distribution differs, and how they become very similar for larger sample sizes. WHY LINEAR MIXED-EFFECTS MODELS ARE PROBABLY NOT THE Linear mixed-effects models are often used for their ability to handle missing data using maximum likelihood estimation. In this post I will present a simple example of when the LMM fails, and illustrate two MNAR sensitivity analyses: the pattern-mixture method and the joint model (shared parameter model). UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
START | R PSYCHOLOGIST powerlmm: Power Analysis for Longitudinal Multilevel Models. The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data. CRAN GitHub.ABOUT KRISTOFFER
About. I'm Kristoffer Magnusson a researcher in clinical psychology at the Centre for Psychiatry Research, Karolinska Institutet, in Stockholm, Sweden. My interests are a mix of open science, gambling problems, statistics, therapist effects, visualization, and psychotherapy. I also have a background in web development, and Istill dabble with
UNDERSTANDING CORRELATIONS An Interactive Visualization. Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are thenVISUALIZATIONS
Posters. I used to sell posters on Etsy, but after making 95 sales (a magic number in science) I decided to stop and share the digital files here for free instead.You can print them in whatever way that fits you. If you want to support me just Buy Me a Coffee or share this page, or print the posters using this affiliate link Printful print-on-demand (it's the company I used when I sold theseBLOG ARCHIVE
Slides from my talk on how to do power analysis for longitudinal 2- and 3-level models. 2018-04-11. UNDERSTANDING P-VALUES A tool to understand p-values using an interactive simulation. the world can never have enough of these beautiful, simple, easily-understood visualizations of basic stats concepts stats is hard for many. i also used to find stats hard. so here's another tools to add to our repertoire, to help build our students' intuitiveunderstanding.
UNDERSTANDING MAXIMUM LIKELIHOOD ESTIMATION Finding the Maximum Likelihood Estimates. Since we use a very simple model, there's a couple of ways to find the MLEs. If we repeat the above calculation for a wide range of parameter values, we get the plots below. The joint MLEs can be found at the top of contour plot, which shows the likelihood function for a grid of parameter values. UNDERSTANDING THE T-DISTRIBUTION AND ITS NORMAL APPROXIMATION Tweet. Most students are told that the t -distribution approaches the normal distribution as the sample size increase, and that the difference is negligible even for moderately large sample sizes (> 30). However, for small samples the difference is important. You might recall that the t -distribution is used when the population varianceis unknown.
INTRODUCING 'POWERLMM' AN R PACKAGE FOR POWER CALCULATIONS Over the years I've produced quite a lot of code for power calculations and simulations of different longitudinal linear mixed models. Over the summer I bundled MEDIATION, CONFOUNDING, AND MEASUREMENT ERROR “The assumptions concerning the lack of hidden confounding and measurement errors are very rarely stated, let alone their validity discussed. One suspects that the majority of investigators are oblivious of these two requirements.rpsychologist-logo
About Posts Visualizations Kristoffer Magnusson PhD, Lic. Clinical Psychologist Hi, I'm Kristoffer, a postdoctoral researcher in clinical psychology. This is my personal page about R, statistics, psychotherapy, open science, and data visualization.BLOG POSTS
HETEROGENEOUS TREATMENT EFFECTS AND HOMOGENEOUS OUTCOME VARIANCES2020-01-10
Recently there has been a couple of meta-analyses investigating heterogeneous treatment effects by analyzing the ratio of theoutcome…
MEDIATION, CONFOUNDING, AND MEASUREMENT ERROR2019-10-09
Mediation might be the ultimate example of how a method continues to be used despite a vast number of papers and textbooks describingthe…
CHANGE OVER TIME IS NOT "TREATMENT RESPONSE"2018-11-19
This will be a non-technical post illustrating the problems with identifying treatment responders or non-responders usinginappropriate…
NEW PAPER: THE CONSEQUENCES OF IGNORING THERAPIST EFFECTS IN LONGITUDINAL DATA ANALYSIS2018-08-24
We just published a paper, The consequences of ignoring therapist effects in trials with longitudinal data: A simulation study , wherewe…
ESTIMATING TREATMENT EFFECTS AND ICCS FROM (G)LMMS ON THE OBSERVED SCALE USING BAYES, PART 1: LOGNORMAL MODELS2018-08-05
When a multilevel model includes either a non-linear transformation (such as the log-transformation) of the response variable, or ofthe…
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PROJECTS
INTERACTIVE VISUALIZATIONS Since 2014 I've created various interactive tools to teach statistics.MAXIMUM LIKELIHOOD
COHEN'S D
STATISTICAL POWER AND SIGNIFICANCE TESTING CONFIDENCE INTERVALSBAYESIAN INFERENCE
CORRELATIONS
EQUIVALENCE AND NON-INFERIORITY TESTING P-VALUE DISTRIBUTIONT-DISTRIBUTION
R SOFTWARE
POWERLMM: POWER ANALYSIS FOR LONGITUDINAL MULTILEVEL MODELS The purpose of powerlmm is to help design longitudinal treatment studies (parallel groups), with or without higher-level clustering (e.g. longitudinally clustered by therapists, groups, or physician), and with missing data.CRAN GitHub
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