# Review 2

When to use each test?

## T-test (one sample)

• Quantity of variables: 1
• Types of variables: continuous
• Null hypothesis: some value (usually sample mean) = population mean

## T-test (independent sample)

• Quantity of variables: 2
• Types of variables: 1 categorical (with 2 categories), 1 continuous
• Null hypothesis: population mean for category 1 = population mean for category 2

## T-test (paired sample)

• Quantity of variables: 2
• Types of variables: 2 continuous (same variables but different time periods)
• Null hypothesis: population mean at time 1 = population mean at time 2

Note: Observations should be paired across time.

## One-way ANOVA

• Quantity of variables: 2
• Types of variables: 1 categorical (with 2 or more categories), 1 continuous.
• Null hypothesis: population mean for category 1 = population mean for category 2 = population mean for category 3 = …

## Two-way ANOVA

• Quantity of variables: 3
• Types of variables: 2 categorical (with 2 or more categories each), 1 continuous.
• Null hypothesis: No interaction between categorical variable 1 and categorical variable 2

Note: In other words, our null is that one categorical variable does not influence the effect of the other categorical variable on our continuous variable.

## Pearson’s correlation

• Quantity of variables: 2
• Types of variables: 2 continuous.
• Null hypothesis: Pearson’s correlation coeff. for the population = 0. Variable1 and variable2 are not correlated.

## Simple linear regression

• Quantity of variables: 2
• Types of variables: 2 continuous (usually)
• Null hypothesis: regression coef. for the population = 0. In other words, our independent variable does not predict our dependent variable.

Note: The key point here is that you have a dependent and an independent variable, meaning that you assume the direction of the relationship. Therefore, regression is more appropriate for predictions.

## Chi-square test for independence

• Quantity of variables: 2 (or more)
• Types of variables: 2 categorical
• Null hypothesis: Variable1 is independent of Variable2.

## Practice questions

Open the “school_data.sav” data set.

Choose the appropriate test for the following questions:

1. Did schools improve their average scores between 1999 and 2000?
2. Does average class size influences average achievement in the year 2000?
3. Is there a relationship between percentage of parents who have completed HS and achievement in a given school?
4. Is there a relationship between percentage of free meals in a given school and whether the school has summer classes?
5. Do California schools with summer classes (year round schools) have higher average achievement?
6. Is the mean achievement for the schools in the sample a good representative of the mean achievement for all California elementary schools?
7. Suppose percentage of free meals are associated with achievement. Does the existence of summer courses in a school influences this relationship?
8. Is average student achievement different between schools with different percentage of free meals?

Hint: Look carefully at the variable labels in your data. Note if the variable is continuous or categorical.