Teaching Statistics Project

CHOOSING A STATISTICAL TEST

Does your data meet the parametric assumptions?

Yes

What do you want to know about the variables?

No

Group Differences

Relationships

Can you transform the data to meet the assumptions?

YES

How many groups are being compared?

Are you trying to make a prediction?

No

No

Yes

3+

How many variables do you have?

Pearson's r Correlation Coefficient

How many dependent variables are there?

3+

t-test

Choose a non-parametric test

2+

Multiple regression

Simple regression

ANOVA

MANOVA

CHOOSING A STATISTICAL TEST

Does your data meet the parametric assumptions?

Yes

What do you want to know about the variables?

No

Group Differences

Relationships

Can you transform the data to meet the assumptions?

YES

How many groups are being compared?

Are you trying to make a prediction?

No

No

Yes

3+

How many variables do you have?

Pearson's r Correlation Coefficient

How many dependent variables are there?

3+

t-test

Choose a non-parametric test

2+

Multiple regression

Simple regression

ANOVA

MANOVA

CHOOSING A STATISTICAL TEST

Does your data meet the parametric assumptions?

Yes

What do you want to know about the variables?

No

Group Differences

Relationships

Can you transform the data to meet the assumptions?

YES

How many groups are being compared?

Are you trying to make a prediction?

No

No

Yes

3+

How many variables do you have?

Pearson's r Correlation Coefficient

How many dependent variables are there?

3+

t-test

Choose a non-parametric test

2+

Multiple regression

Simple regression

ANOVA

MANOVA

Parametric Assumptions

1. The dependent variable is measured on an interval or ratio scale
2. The dependent variable has independent scores (i.e., the scores of one participant do not influence the scores of another)
3. The data is normally distributed (or close to normal)
4. 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 t-tests

Independent groups

• 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

Paired samples

• 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

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?

ANOVA

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.

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?

MANOVA

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.

Non-parametric tests

The following are situations in which a non-parametric test might be more appropriate than a parametric test.

• 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 are considered less powerful than parametric tests, so a parametric test should be applied whenever possible.

Non-parametric tests

The following are situations in which a non-parametric test might be more appropriate than a parametric test.

• 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 are considered less powerful than parametric tests, so a parametric test should be applied whenever possible.

Parametric Assumptions

1. The dependent variable is measured on an interval or ratio scale
2. The dependent variable has independent scores (i.e., the scores of one participant do not influence the scores of another)
3. The data is normally distributed (or close to normal)
4. 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 t-tests

Independent groups

• 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

Paired samples

• 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

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?

ANOVA

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.

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?

MANOVA

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.

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

The following are situations in which a non-parametric test might be more appropriate than a parametric test.

• 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 are considered less powerful than parametric tests, so a parametric test should be applied whenever possible.

Parametric Assumptions

1. The dependent variable is measured on an interval or ratio scale
2. The dependent variable has independent scores (i.e., the scores of one participant do not influence the scores of another)
3. The data is normally distributed (or close to normal)
4. 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 t-tests

Independent groups

• 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

Paired samples

• 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

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?

ANOVA

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.

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?

MANOVA

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.

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?