4.1

T tests are statistical tests used to compare means or average scores of two groups or conditions.

One Sample T Test
- Compares the sample mean to a population mean.
- Example: Comparing the mean score of a group on a DAS (Dementia Assessment Scale) to the average score of the broader population.
Independent Samples T Test
- Used for two completely separate groups.
- Example: Comparing an experimental group and a control group in a study where participants are not related or paired.
Paired Samples T Test
- Used when the same participants are measured under two different conditions or at two different time points.
- Also referred to as a within-subject design or repeated measures design.

Parametric Test: Assumes certain conditions about the data and population distributions.
Independent Variable: Categorical variable with two groups or conditions.
Dependent Variable: Continuous variable that can be measured on a continuous scale.

There will be a difference in the average score between the two groups:
$H_1: ext{Mean of Group One} <br>eq ext{Mean of Group Two}$

There will be no difference between the two means:
$H_0: ext{Mean of Group One} = ext{Mean of Group Two}$

Independence of Observations:
- Scores within the groups must be independent. No participant should influence another participant's score.
Continuous Dependent Variable:
- The dependent variable must be measurable on a continuous scale.
Normality:
- The dependent variable should follow a normal distribution (bell curve).
- Methods to test include QQ plots, histograms, and statistical tests (e.g., Shapiro-Wilk test).
Homogeneity of Variance:
- The variances within each group must be approximately equal.
- Test using Levine's test.

If any of the assumptions are violated:
1. Use transformations to correct normality (e.g., square root, logarithm).
2. Switch to non-parametric tests (e.g., Mann-Whitney U test for independent samples).

Run the Test: Analyze the data and compute the T statistic, degrees of freedom, P-value, and effect size (Cohen’s D).
Interpret the Results:
- For statistically significant results (P < 0.05), reject the null hypothesis.
- For non-significant results (P > 0.05), fail to reject the null hypothesis.
Cohen’s D Interpretation:
- Small (0.2), Medium (0.5), Large (0.8) effects to understand the practical significance of results.

Report essential statistics:
- T statistic, degrees of freedom, P-value, and effect size in APA format.
Example APA interpretation: "An independent samples t-test indicated there was no significant difference between the control group and the experimental group, t(df) = value, p = value, Cohen’s D = value."
Utilize plots/figures to represent data visually and enhance clarity in results.

An extension of the T-test for comparing three or more group means.
Advantages include better control of type I error rates (family-wise error rates).
Requires:
- Categorical independent variable (three or more conditions) and continuous dependent variable.
F statistic compares variance within and between groups.

Used after a significant ANOVA to determine which groups differ from one another.
Common methods include Tukey's HSD (control type I error) and Bonferroni tests (more conservative approach).

Always check for a significant ANOVA before post hoc tests. If ANOVA is significant (P < 0.05), proceed with follow-up analyses.
Ensure clear reporting that includes direction and significance of any group differences.

The independent samples T test is used when comparing group means for two categories of a continuous variable, under the assumptions of independence, normality, and homogeneity of variance.
When comparing more than two groups, use ANOVA with the necessary follow-up post hoc tests to identify specific differences.
Proper assumptions checks and reporting are essential to maintaining statistical integrity in research.