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# T-Test PowerPoint PPT Presentation

T-Test. The purpose of t test (Gosset, 1908) is to compare two means. It assesses whether two means are statistically different. It can assess the difference between two groups or two variables. Limitations.

T-Test

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### T-Test

• The purpose of t test (Gosset, 1908) is to compare two means.

• It assesses whether two means are statistically different.

• It can assess the difference between two groups or two variables.

### Limitations

• It assumes that the data are normally distributed (e.g., Wilk-Shapiro normality test)

• It assumes that there is equality of variances between groups (e.g., F test, or more robust Levene's test)

• It is highly sensitive to sample sizes (need n>30)

• It only can be used to compare two groups. If used to compare more than 2 groups, we may incur a type-I error.

### T-Test Models

• Independent-samples t test (independent means): Compares the means of one variable for two groups.

• Paired-samples t test (dependent means): Compares the means of two variables for a single group.

### Independent-samples t test

• It compares means for two groups of cases.

• Used in survey studies with different groups (e.g., teachers and administrators) to assess whether there are differences in responses or scores between the two groups.

### Example - Independent Samples

• Used in experimental studies, in which subjects are randomly assigned to two groups (treatment and control), to assess whether differences are found between groups before the intervention (equivalence)

• Question: Are the two groups of students (treatment and control) the same on key characteristics (e.g., reading pre-test score) before the intervention?

### Procedures

• Analyze

Compare means

Independent-samples t test

Test variables: select the variables

Grouping variable: select the group variable

Define groups: type codes

(e.g., control=0, treatment=1)

Click Continue, then OK

### An example

• Dataset: Survey3ED.sav (Pallant)

• Use t test to assess whether there are significant differences between males and females on their self-esteem levels

• The grouping variable will be: Gender.

• Check data (Ns for each group, missing data? Coding?)

• Check assumptions (e.g., Levene’s test for equality of variances)

### Survey3ED example (continued)

• Assess differences between groups

• Calculate effect sizes

• Present results

### Are we having fun?

• Based on your research interests, what research questions would require an independent samples t-test?

• Try it out!

### Paired-samples t test

• It is commonly used in quasi-experimental or "pre-post" design.

• Pre-post designs consists of two measurements taken on the same subjects, one before and one after the introduction of a treatment or intervention.

• If the treatment had no effect, the average difference between the measurements is equal to 0 and the null hypothesis holds.

• If the treatment had an effect (intended or unintended!), the average difference is not 0 and the null hypothesis is rejected.

### Example Paired-Samples

• Used in experimental studies, in which subjects are randomly assigned to two groups (treatment and control), to assess whether differences are found between groups after the intervention (pre-post impact)

• Research Question: Will students randomly assigned to the reading intervention improve their reading outcomes significantly more than students randomly assigned to the control group?

### Procedures

• Analyze

Compare Means

Paired-Samples T Test

Paired variables: Select pre-post variables

Options:

Confidence interval: 95%

Missing values: exclude cases analysis by analysis

### An example

• Dataset: experim3ED.sav (Pallant)

• Use t test to assess whether there are significant differences between students’ confidence in their ability to successfully complete a statistics course following the intervention.

• The grouping variable will be: Time.

• Check data (Ns for each group, missing data? Coding?)

• Check assumptions (e.g., Levene’s test for equality of variances, plus difference between scores are normally distributed, n>30)

Experim3ED example (cont.)

• Determine overall significance (p<.05)

• Compare mean values – which is higher? T1 or T2?

• Limitation: No treatment/control groups

• PCVs – Potentially confounding variables

• Calculate effect size

• Present results

### Are we (still) having fun?

• Based on your research interests, what research questions would require a paired samples t-test?

• Try it out!