Understanding One-Tailed and Two-Tailed T-Tests

One-Tailed Test

Tests if the mean is significantly greater or less than a predetermined value in one direction.

Two-Tailed Test

Tests if the mean is different (either greater or less) from a predetermined value.

One-Tailed Null Hypothesis

μ ≥5 (mean ≥5)

One-Tailed Alternative Hypothesis

μ < 5 (mean < 5)

Two-Tailed Null Hypothesis

μ = 75 (mean = 75)

Two-Tailed Alternative Hypothesis

μ ≠75 (mean ≠75)

Independent Samples T-Test

Compares the means of two separate groups.

Dependent Samples T-Test

Compares means of two related groups (before and after).

T-Value

A larger t value (in absolute terms) indicates a greater difference between groups.

Degrees of Freedom (df)

df = (n₁ + n₂) −2, where n₁ and n₂ are the number of participants in groups A and B, respectively.

Example for df Calculation

df = (50 in sample A + 52 in sample B) −2 = 102 −2 = 100.

Type I Error

A Type I error occurs when the researcher rejects the null hypothesis when it is actually true.

Bonferroni Procedure

Adjusts for Type I error by dividing the alpha level by the number of t-tests conducted.

Corrected alpha Calculation

If alpha = 0.05 and 5 t-tests are conducted: Corrected alpha = 0.05 ÷ 5 = 0.01.

Normal Distribution

Raw scores in the population should be normally distributed.

Level of Measurement

The dependent variable(s) must be measured at the interval or ratio levels.

Equal Variance

The two groups should have equal variance, which is best achieved by random sampling and random assignment.

Independence of Scores

Observations within each group must be independent or unrelated to each other.

Paired Samples t-Test

Determines differences between two sets of repeated measures data from one group of individuals.

One-group pretest-posttest design

Participants undergo a pretest, treatment/intervention, and posttest.

Cross-Over Design

Paired samples t-tests are applied to crossover study designs where participants receive two different treatments or interventions.

Normality for Paired Samples t-Test

The distribution of scores should be normal or approximately normal.

Independence of Differences

The differences between paired scores must be independent of each other.

Matching Participants

Cases and controls are matched for variables like age, diagnosis, or severity of illness.

Weakness of One-group Design

One-group design is a weak quasi-experimental design, as it lacks a separate control group for comparison.

Simplicity of t-Test

The t-test is the simplest statistic for comparing two means.