. Each of the following sets of sample statistics comes from a within- subjects design.

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### Transcription of Image for Educational Website

#### Source: Lab Manual for Statistical Analysis — Dawn M. McBride, J. Cooper Cutting

---

#### Table: Handedness Scores of Twin Pairs

| Pair | Twin A | Twin B |
|------|--------|--------|
| 1    | +10    | +11    |
| 2    | -8     | +3     |
| 3    | -11    | +11    |
| 4    | +15    | +10    |
| 5    | 0      | +8     |
| 6    | -4     | +7     |

---

#### Analysis Task

4. **Question:**
   Each of the following sets of sample statistics comes from a within-subjects design.

   **Set 1:** 
   - \( n = 10 \)
   - \( \overline{D} = +4.0 \)
   - \( s = 10 \)

   **Set 2:**
   - \( n = 10 \)
   - \( \overline{D} = +4.0 \)
   - \( s = 2 \)

   **Task:**
   Find t values. Without looking up the critical t, for which set is it more likely to reject the \( H_0 \) indicating that the \( \mu_D = 0 \)? Why?

---

### Section 32: Related Samples T Test in SPSS

---

#### Explanation:

The table above presents handedness scores for twin pairs, indicating each twin's score for six pairs. These scores can be analyzed for statistical differences within pairs. The related samples t-test is used to determine if there is a significant difference between the means of two related groups. In this case, those groups are the scores of Twin A and Twin B across pairs.

The task given involves two sets of sample statistics to assess which is more likely to reject the null hypothesis \( H_0 \), assuming \( \mu_D = 0 \) (the population mean difference is zero). The decision is based on comparing the mean differences and standard deviations across the sample sizes provided. 

Set 1 and Set 2 both have the same mean difference but different standard deviations, with Set 2 having a smaller standard deviation, which makes it more likely to achieve statistical significance given the same size \( n \).

---
Transcribed Image Text:### Transcription of Image for Educational Website #### Source: Lab Manual for Statistical Analysis — Dawn M. McBride, J. Cooper Cutting --- #### Table: Handedness Scores of Twin Pairs | Pair | Twin A | Twin B | |------|--------|--------| | 1 | +10 | +11 | | 2 | -8 | +3 | | 3 | -11 | +11 | | 4 | +15 | +10 | | 5 | 0 | +8 | | 6 | -4 | +7 | --- #### Analysis Task 4. **Question:** Each of the following sets of sample statistics comes from a within-subjects design. **Set 1:** - \( n = 10 \) - \( \overline{D} = +4.0 \) - \( s = 10 \) **Set 2:** - \( n = 10 \) - \( \overline{D} = +4.0 \) - \( s = 2 \) **Task:** Find t values. Without looking up the critical t, for which set is it more likely to reject the \( H_0 \) indicating that the \( \mu_D = 0 \)? Why? --- ### Section 32: Related Samples T Test in SPSS --- #### Explanation: The table above presents handedness scores for twin pairs, indicating each twin's score for six pairs. These scores can be analyzed for statistical differences within pairs. The related samples t-test is used to determine if there is a significant difference between the means of two related groups. In this case, those groups are the scores of Twin A and Twin B across pairs. The task given involves two sets of sample statistics to assess which is more likely to reject the null hypothesis \( H_0 \), assuming \( \mu_D = 0 \) (the population mean difference is zero). The decision is based on comparing the mean differences and standard deviations across the sample sizes provided. Set 1 and Set 2 both have the same mean difference but different standard deviations, with Set 2 having a smaller standard deviation, which makes it more likely to achieve statistical significance given the same size \( n \). ---
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