Dependent Sample t-Test

Dependent Sample t-Test (Repeated-Measures Design aka. Within-Subject Design)

Used to study phenomena that are expressed as differences among behavioral measures at different times (learning, forgetting, attitude change, etc.)

• A single sample of individuals is measured multiple times on the same dependent variable

- Often used to track changes in a dependent variable over time

o Repeated procedures with the same individual (Exam 1 vs. Exam 2) OR (Pre-test vs. Post-test)

FORMULA:

t = D - μ_D / s_D̄

basically in simple sense its → t = D / s_D/√N

D → X_1 - X_2 ; → D= ∑D/n ; D is the mean of the difference scores

s_D → s_D = √SS / n-1 ; is the standard devation of difference scores

s_D̄ → s_D̄ = s_D/√n ; is the estimated standard error of difference scores

NOTE: df = N-1

• N in the FORMULA = total number of difference scores (or the number of pairs, not the number of raw scores)

Matched Subjects

• each individual in one sample is matched with an individual in another sample

- matching → two individuals are the same with respect to a specific variable, such as age, gender, IQ, that the researcher would like to control

o Participants in each group are the same, related, or matched (husbands and wives, siblings, twins)

Repeated-Measures Advantages

• More efficient

- Uses far less cases than a corresponding randomized-group design

- More data can be controlled in a short period of time

• Increased control of subjects variability (matched data)

• Control individual variability among participants that can contribute to an error (increases power of study)

Repeated Measures Limitations

• lack of independence

• repeated observations can affect scores (practice and fatigue effect)

• Using different materials to reduce practice may be needed which may make the experiment less controlled

• Lingering effect of drug treatment

• Participant drop-out

• Complicated to set up

Dependent samples t-test EXAMPLE

1. Find D

• D = ∑D/n → -64/4 = -16

2. Find s_D

• s_D = √SS / n-1 → √596/4-1 = 14.09

3. find s_D̄

• s_D̄ = s_D/√n → 14.09/√4 = 7.05

4. find dependent sample t

• t = D/S_D̄ → -16/7.05 = -2.27

5. Interpret

• Critical Region

- n = 4

- df = 4-1 =3

- 5_.025 (3) = ± 3.182

o t-value < critical value → retain H_0

7. APA Style

Fail to reject the null hypothesis. On average, drinking one alcoholic beverage does not significantly affect an individual’s reaction time,

t(3) = -2.27, p > .05.