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Dependent Samples t test

2.1. Dependent Samples t test

Dependent Samples t Test

Types of Related Samples

There are three types of related samples which are appropriate for the Dependent Samples t Test.

Gist: There is some sort of known meaningful relationship between the two groups of scores.

Similiar to previous tests, but...

2.2. Dependent Samples t Test Example

NHST Example

Step 1: State the Null and Alternative Hypotheses

Define the populations: Relationship Satisfaction = RS

State the Hypotheses: Note the directional alternative hypothesis; pay careful attention to how we specified the hypotheses in symbols.

Step 2: Comparison Distribution (estimate \(\sigma\) with \(S_M\)).

Pair Before After \(D\) \(\overline{D}\) \((D - \overline{D})\) \(\left(D - \overline{D}\right)^2\)
1 40 32 8 8 0 0
2 38 31 7 8 -1 1
3 36 30 6 8 -2 4
4 42 31 11 8 3 9
4 32 \(SOS = 14\)


\(\overline{D} = \sum(D)/n_D = 32/4 = 8\)


\(S^2 = SOS/df = 14/n_D - 1 = 14/3 = 4.67\)


\(S_M^2 = \frac{S^2}{n_D} = \frac{4.67}{4} = 1.1675\)


\(S_M = \sqrt{S_M^2} = \sqrt{1.1675} = 1.08\)

Step 3: Determine the critical value

Step 4: Calculate t

\(t = \frac{\overline{X} - \mu}{S_M}\)
\(t = \frac{\overline{D} - \mu_D}{S_M} = \frac{8 - 0}{1.08} = 7.41\)

Step 5: Compare and make a decision.

Image M8_001

2.3. Effect Size

Effect Size

\(d = \frac{\overline{X} - \mu}{\sigma}\)
\(d = \frac{\overline{D} - \mu_D}{S}\)

Effect Size continued

\(d = \frac{\overline{D} - \mu_D}{S}\)
\(S = \sqrt{4.67} = 2.16\)
\(d = \frac{\overline{D} - \mu_D}{S} = \frac{8 - 0}{2.16} = 3.70\)

2.4. Using Delta for Power

Using Delta (\(\delta\)) for Statistical Power

\(\delta = d * \sqrt{\frac{n}{2}}\)
\(\delta = d * \sqrt{\frac{n}{2}} = 3.7 * \sqrt{\frac{4}{2}} = 3.7 * \sqrt{2} = 3.7 * 1.414 = 5.233\)
http://www.unt.edu/rss/class/Jon/ISSS_SC/Module008/delta

Using Delta \(\delta\) to calculate appropriate sample size

http://www.unt.edu/rss/class/Jon/ISSS_SC/Module008/delta

2.5. \(CI_{95}\)

Calculating a Confidence Interval with \(\overline{D}\)

\(LL = -t_{crit}*{S_M} + \overline{D} = -2.353 * 1.08 + 8 = -2.541 + 8 = 5.459\)



\(UL = +t_{crit}*{S_M} + \overline{D} = +2.353 * 1.08 + 8 = +2.541 + 8 = 10.541\)

Interpretation of \(CI_{95}\)

2.6. Summary of Section 2

Dependent Samples t Test Usage?

Fortunately...

Summary of Section 2

Section 2 covered the following topics:


next up previous contents
Next: Independent Up: Module 8: Introduction to Previous: One Sample   Contents
jds0282 2010-10-15