T-Tests

Purpose:

Compare the means between two groups. There are three kinds of t-tests: an independent samples t-test (for between-group manipulation), repeated measures t-test (for within-group manipulation), and a one-sample t-tests (for one sample being compared to the population).

Note: Between-group manipulation (between-subjects study design) means that each group received a different IV treatment condition (level). Within-group manipulation (within-subjects study design) means that every participant experiences every IV treatment condition (level).

Context used:

• There must be only ONE CATEGORICAL IV, with only TWO LEVELS.

• Additionally, there must be only ONE QUANTITATIVE DV.

Note: Categorical variables are variables where the data represents groups with no real numerical value (e.g., gender, car brand, hair color, eduction level). Quantitative variables are variables where the data represents amounts with a real numerical value (e.g., height, weight, age, time, speed, distance).

Jamovi Walkthrough:

Independent Samples T-test:

1. Click "T-Tests"

2. Click "Independent Samples T-test"

3. Enter the qualitative dependent variable into "Dependent Variables" box

4. Enter the categorical independent variable in "Group Variable" box

5. Check "Effect size" under "Additional Statistics"

Repeated Measures T-test:

1. Click "T-Tests"

2. Click "Paired Samples T-Test"

3. Enter the two IV level scores into the "Paired Variables" box

4. Check "Effect size" under "Additional Statistics"

One-Sample T-test:

1. Click "T-Tests"

2. Click "One Sample T-Test"

3. Enter the two DV scores of the sample and population into the "Dependent Variables" box

4. Check "Effect size" under "Additional Statistics"

Output Interpretation:

p-value: The probability that you detect a meaningful relationship/difference when there is none. We are typically looking for a small value (p < 0.5).

If p < 0.5, reject the null hypothesis. There IS a difference.

If p > 0.5, accept the null hypothesis. There is NO difference.

t-value: The number of estimated standard error of the mean (SEM) units the sample is from the population.

If t-value is small, there is more similarity between the two sample sets.

If t-value is large, a large difference exists between the two sample sets.

If t-value is negative, it has no bearing on the significance of the difference. It only indicates a reversed directionality of the effect.

SEM: Average deviation of sample means from the population mean. A measure of sampling error

If SEM is small, sample means are similar to the population mean, with little sampling error (This is what we want).

If SEM is large sample means are variable.

df: Values in a study that have the freedom to vary and are essential for assessing the importance and validity of the null hypothesis. 

Effect size: A measure of the magnitude of the mean difference. Bigger numbers mean a bigger difference between groups in terms of standard deviation. 

If Cohen's D = 0.20-0.49, small effect size.

If Cohen's D = 0.50-0.79, medium effect size

If Cohen's D = 0.80+, large effect size.

APA Format:

Appropriate data visualization: Bar graphs (with error bars).

Sample table: https://apastyle.apa.org/style-grammar-guidelines/tables-figures/sample-tables#tests

Sample write-up:

A paired-sample t-test compared the average number of apples eaten by a sample of students during freshman year with the average number of apples eaten by the sample of students during their senior year. There was a significant difference in the number of apples eaten by freshmen (M=  SD=) and seniors (M=  SD=  ); t(df )=X , p<0.5, n²=   . These results suggest that number of apples eaten increases from freshman to senior year. 

Note: plugin the appropriate test used, means, standard deviations, whether the test was significant, t-value, df, p-level, the strength of the relationship (n²), and a conclusion.