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Teaching Statistics Project
Kiley Komnik
Created on November 16, 2024
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Transcript
ANOVA
Pearson's r Correlation Coefficient
Can you transform the data to meet the assumptions?
Choose a non-parametric test
Relationships
Group Differences
What do you want to know about the variables?
Does your data meet the parametric assumptions?
3+
How many dependent variables are there?
2+
t-test
Simple regression
Multiple regression
How many groups are being compared?
3+
MANOVA
How many variables do you have?
Yes
Are you trying to make a prediction?
No
No
YES
No
CHOOSING A STATISTICAL TEST
Yes
CHOOSING A STATISTICAL TEST
ANOVA
Pearson's r Correlation Coefficient
Can you transform the data to meet the assumptions?
Choose a non-parametric test
Relationships
Group Differences
What do you want to know about the variables?
Does your data meet the parametric assumptions?
3+
How many dependent variables are there?
2+
t-test
Simple regression
Multiple regression
How many groups are being compared?
3+
MANOVA
How many variables do you have?
Yes
Are you trying to make a prediction?
No
No
YES
No
Yes
CHOOSING A STATISTICAL TEST
ANOVA
Pearson's r Correlation Coefficient
Can you transform the data to meet the assumptions?
Choose a non-parametric test
Relationships
Group Differences
What do you want to know about the variables?
Does your data meet the parametric assumptions?
3+
How many dependent variables are there?
2+
t-test
Simple regression
Multiple regression
How many groups are being compared?
3+
MANOVA
How many variables do you have?
Yes
Are you trying to make a prediction?
No
No
YES
No
Yes
Parametric Assumptions
- The dependent variable is measured on an interval or ratio scale
- The dependent variable has independent scores (i.e., the scores of one participant do not influence the scores of another)
- The data is normally distributed (or close to normal)
- There is homogeneity of variance (i.e., the variance of the DV needs to be the same at each level of the IV)
- Types of variables: 1 categorical IV with 2 levels, 1 continuous DV
- What it does: Compares the means of 2 dependent groups
- Think: within-subjects design, repeated measures
Paired samples
- Types of variables: 1 categorical IV with 2 levels, 1 continuous DV
- What it does: Compares the means of 2 different groups
- Think: between-subjects design, independent measures
Independent groups
Types of t-tests
Multiple regression
- Types of variables: 1 continuous dependent/outcome variable, and multiple continuous indpendent/predictor variables
- What it does: Provides an equation to predict the outcome of one variable based on multiple othe variables.
- Example question: What is the combined effect of hours spent studying per week, hours of sleep per night, and hours of phone use per day on a student's GPA?
Types of Variables: 1 or more categorical indpendent variables with 2 or more levels, and 1 continuous dependent variable What it does: Compares the means of 3 or more groups to determine if a statistically significant difference exists One-way ANOVA: 1 categorical IV; compares means of a continuous DV Two-way ANOVA: 2 categorical IVs; tests for individual effects of the IVs on the DV, as well as for interactions Repeated measures ANOVA: compares the means of one participant across different groups Example question: Do happiness levels significantly differ based on attachment style (secure, anxious, avoidant, disorganized)? While an ANOVA test can tell us that a significant difference exists between groups, post hoc tests must be conducted to determine where the difference is. Examples of post-hoc tests are Tukey’s HSD and the Bonferroni Correction.
ANOVA
Simple regression
- Types of variables: 2 continuous variables
- What it does: Provides an equation that can be used to predict the outcome of one variable based on another
- Example question: What is a person's expected GPA if they study 10 hours per week?
Pearson's r
- Types of variables: 2 continuous variables
- What it does: Measures the strength and direction of the linear relationship
- Example question: Is there a significant relationship between the number of hours students spend studying per week and their GPA?
Types of Variables: 1 or more categorical indpendent variables with 2 or more levels, and 2 or more continuous dependent variablesWhat it does: Compares the means of multiple dependent variable across groups to determine if a statistically significant difference exists Example question: Does someone's attachment style (secure anxious, avoidance, disorganized) significantly affect their emotional well-being and sense of social connectedness? While a MANOVA test can tell us that a significant difference exists between groups, post hoc tests must be conducted to determine where the difference is. Examples of post-hoc tests are Tukey’s HSD and the Bonferroni Correction.
MANOVA
Non-parametric tests are considered less powerful than parametric tests, so a parametric test should be applied whenever possible.
- The data has a non-normal distribution
- And therefore, when the median is more representative than the mean
- The dependent/outcome variables are categorical
- There are outliers or extreme values
- The sample size is small
Non-parametric tests
The following are situations in which a non-parametric test might be more appropriate than a parametric test.
Non-parametric tests are considered less powerful than parametric tests, so a parametric test should be applied whenever possible.
- The data has a non-normal distribution
- And therefore, when the median is more representative than the mean
- The dependent/outcome variables are categorical
- There are outliers or extreme values
- The sample size is small
Non-parametric tests
The following are situations in which a non-parametric test might be more appropriate than a parametric test.
Parametric Assumptions
- The dependent variable is measured on an interval or ratio scale
- The dependent variable has independent scores (i.e., the scores of one participant do not influence the scores of another)
- The data is normally distributed (or close to normal)
- There is homogeneity of variance (i.e., the variance of the DV needs to be the same at each level of the IV)
- Types of variables: 1 categorical IV with 2 levels, 1 continuous DV
- What it does: Compares the means of 2 dependent groups
- Think: within-subjects design, repeated measures
Paired samples
- Types of variables: 1 categorical IV with 2 levels, 1 continuous DV
- What it does: Compares the means of 2 different groups
- Think: between-subjects design, independent measures
Independent groups
Types of t-tests
Multiple regression
- Types of variables: 1 continuous dependent/outcome variable, and multiple continuous indpendent/predictor variables
- What it does: Provides an equation to predict the outcome of one variable based on multiple othe variables.
- Example question: What is the combined effect of hours spent studying per week, hours of sleep per night, and hours of phone use per day on a student's GPA?
Types of Variables: 1 or more categorical indpendent variables with 2 or more levels, and 1 continuous dependent variable What it does: Compares the means of 3 or more groups to determine if a statistically significant difference exists One-way ANOVA: 1 categorical IV; compares means of a continuous DV Two-way ANOVA: 2 categorical IVs; tests for individual effects of the IVs on the DV, as well as for interactions Repeated measures ANOVA: compares the means of one participant across different groups Example question: Do happiness levels significantly differ based on attachment style (secure, anxious, avoidant, disorganized)? While an ANOVA test can tell us that a significant difference exists between groups, post hoc tests must be conducted to determine where the difference is. Examples of post-hoc tests are Tukey’s HSD and the Bonferroni Correction.
ANOVA
Simple regression
- Types of variables: 2 continuous variables
- What it does: Provides an equation that can be used to predict the outcome of one variable based on another
- Example question: What is a person's expected GPA if they study 10 hours per week?
Types of Variables: 1 or more categorical indpendent variables with 2 or more levels, and 2 or more continuous dependent variablesWhat it does: Compares the means of multiple dependent variable across groups to determine if a statistically significant difference exists Example question: Does someone's attachment style (secure anxious, avoidance, disorganized) significantly affect their emotional well-being and sense of social connectedness? While a MANOVA test can tell us that a significant difference exists between groups, post hoc tests must be conducted to determine where the difference is. Examples of post-hoc tests are Tukey’s HSD and the Bonferroni Correction.
MANOVA
Pearson's r
- Types of variables: 2 continuous variables
- What it does: Measures the strength and direction of the linear relationship
- Example question: Is there a significant relationship between the number of hours students spend studying per week and their GPA?
Non-parametric tests are considered less powerful than parametric tests, so a parametric test should be applied whenever possible.
- The data has a non-normal distribution
- And therefore, when the median is more representative than the mean
- The dependent/outcome variables are categorical
- There are outliers or extreme values
- The sample size is small
Non-parametric tests
The following are situations in which a non-parametric test might be more appropriate than a parametric test.
Parametric Assumptions
- The dependent variable is measured on an interval or ratio scale
- The dependent variable has independent scores (i.e., the scores of one participant do not influence the scores of another)
- The data is normally distributed (or close to normal)
- There is homogeneity of variance (i.e., the variance of the DV needs to be the same at each level of the IV)
- Types of variables: 1 categorical IV with 2 levels, 1 continuous DV
- What it does: Compares the means of 2 dependent groups
- Think: within-subjects design, repeated measures
Paired samples
- Types of variables: 1 categorical IV with 2 levels, 1 continuous DV
- What it does: Compares the means of 2 different groups
- Think: between-subjects design, independent measures
Independent groups
Types of t-tests
Multiple regression
- Types of variables: 1 continuous dependent/outcome variable, and multiple continuous indpendent/predictor variables
- What it does: Provides an equation to predict the outcome of one variable based on multiple othe variables.
- Example question: What is the combined effect of hours spent studying per week, hours of sleep per night, and hours of phone use per day on a student's GPA?
Types of Variables: 1 or more categorical indpendent variables with 2 or more levels, and 1 continuous dependent variable What it does: Compares the means of 3 or more groups to determine if a statistically significant difference exists One-way ANOVA: 1 categorical IV; compares means of a continuous DV Two-way ANOVA: 2 categorical IVs; tests for individual effects of the IVs on the DV, as well as for interactions Repeated measures ANOVA: compares the means of one participant across different groups Example question: Do happiness levels significantly differ based on attachment style (secure, anxious, avoidant, disorganized)? While an ANOVA test can tell us that a significant difference exists between groups, post hoc tests must be conducted to determine where the difference is. Examples of post-hoc tests are Tukey’s HSD and the Bonferroni Correction.
ANOVA
Simple regression
- Types of variables: 2 continuous variables
- What it does: Provides an equation that can be used to predict the outcome of one variable based on another
- Example question: What is a person's expected GPA if they study 10 hours per week?
Types of Variables: 1 or more categorical indpendent variables with 2 or more levels, and 2 or more continuous dependent variablesWhat it does: Compares the means of multiple dependent variable across groups to determine if a statistically significant difference exists Example question: Does someone's attachment style (secure anxious, avoidance, disorganized) significantly affect their emotional well-being and sense of social connectedness? While a MANOVA test can tell us that a significant difference exists between groups, post hoc tests must be conducted to determine where the difference is. Examples of post-hoc tests are Tukey’s HSD and the Bonferroni Correction.
MANOVA
Pearson's r
- Types of variables: 2 continuous variables
- What it does: Measures the strength and direction of the linear relationship
- Example question: Is there a significant relationship between the number of hours students spend studying per week and their GPA?