Problem 2: The items below are based on the following scenario. A social psychologist conducted a study to answer the question, "Does Smith's rehabilitation program decrease the rate of prisoners who re-offend?" The results and an excerpt from the results section of this fictional study follow: A chi-square test for independence was conducted to test whether Smith's rehabilitation program differed from the old system in the number of repeat offenders. Results indicated that a difference did exist, χ 2 (1, N = 68) = 8.74, p < .01. The phi coefficient for this study was ______.

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Problem 2: The items below are based on the following scenario. A social psychologist conducted a study to answer the question, "Does Smith's rehabilitation program decrease the rate of prisoners who re-offend?" The results and an excerpt from the results section of this fictional study follow:

A chi-square test for independence was conducted to test whether Smith's rehabilitation program differed from the old system in the number of repeat offenders. Results indicated that a difference did exist, χ 2 (1, N = 68) = 8.74, p < .01.

The phi coefficient for this study was ______.

The table presents data on observed and expected frequencies concerning re-offending rates across two programs. Below is the detailed transcription and explanation of the table:

**Table Title:**
Observed (and Expected) Frequencies

**Columns:**
- **Program**: Lists the two programs under evaluation: Smith's and Standard.
- **Re-Offend?**: Divides into two categories: No and Yes, indicating whether participants re-offended.
- **Total**: Indicates the total number of participants in each program.
- **Percent**: Shows the percentage of participants in each program out of the total participants.

**Rows:**
- **Smith's**
  - **No**: Observed frequency is 8, with an expected frequency of (14).
  - **Yes**: Observed frequency is 26, with an expected frequency of (20).
  - **Total**: 34 participants in Smith’s program, representing 50% of the total participants.
  
- **Standard**
  - **No**: Observed frequency is 20, with an expected frequency of (14).
  - **Yes**: Observed frequency is 14, with an expected frequency of (20).
  - **Total**: 34 participants in the Standard program, also representing 50% of the total participants.

**Overall Totals:**
- **No**: 28 did not re-offend.
- **Yes**: 40 re-offended.
- **Total**: 68 participants overall, with percentages rounding up to 100%.

**Interpretation:**
The expected frequencies are placed in parentheses and indicate the number predicted by statistical calculations if there was no difference between programs. The comparison between observed and expected frequencies shows deviation in actual re-offending behavior from the statistical expectation in both programs.
Transcribed Image Text:The table presents data on observed and expected frequencies concerning re-offending rates across two programs. Below is the detailed transcription and explanation of the table: **Table Title:** Observed (and Expected) Frequencies **Columns:** - **Program**: Lists the two programs under evaluation: Smith's and Standard. - **Re-Offend?**: Divides into two categories: No and Yes, indicating whether participants re-offended. - **Total**: Indicates the total number of participants in each program. - **Percent**: Shows the percentage of participants in each program out of the total participants. **Rows:** - **Smith's** - **No**: Observed frequency is 8, with an expected frequency of (14). - **Yes**: Observed frequency is 26, with an expected frequency of (20). - **Total**: 34 participants in Smith’s program, representing 50% of the total participants. - **Standard** - **No**: Observed frequency is 20, with an expected frequency of (14). - **Yes**: Observed frequency is 14, with an expected frequency of (20). - **Total**: 34 participants in the Standard program, also representing 50% of the total participants. **Overall Totals:** - **No**: 28 did not re-offend. - **Yes**: 40 re-offended. - **Total**: 68 participants overall, with percentages rounding up to 100%. **Interpretation:** The expected frequencies are placed in parentheses and indicate the number predicted by statistical calculations if there was no difference between programs. The comparison between observed and expected frequencies shows deviation in actual re-offending behavior from the statistical expectation in both programs.
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