The following SPSS output examines the percent of security staff that is female at private and public prisons. Based on the output answer the question below.       Assuming the difference was significant, what is the effect size based on a calculated r2?     A small difference between the prisons     A moderate difference between the prisons     A large difference between the prisons

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  1. The following SPSS output examines the percent of security staff that is female at private and public prisons. Based on the output answer the question below.
     

     

     
    Assuming the difference was significant, what is the effect size based on a calculated r2?
       
    A small difference between the prisons
       
    A moderate difference between the prisons
       
    A large difference between the prisons
### Analysis of Female Security Staff Percentages in Public and Private Prisons

#### Group Statistics

| Facility Type | N     | Mean    | Std. Deviation | Std. Error Mean |
|---------------|-------|---------|----------------|-----------------|
| Public        | 1302  | 25.4351 | 18.34235       | 0.50833         |
| Private       | 343   | 43.3830 | 21.01978       | 1.13496         |

This table displays the mean percentage of female security staff in public and private prison facilities. Public facilities show a mean of 25.44% with a standard deviation of 18.34, while private facilities have a mean of 43.38% with a standard deviation of 21.02.

#### Independent Samples Test

| Test                              | F      | Sig. | t      | df     | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference |
|-----------------------------------|--------|------|--------|--------|-----------------|-----------------|-----------------------|------------------------------------------|
| Levene's Test for Equality of Variances | 12.924 | .000 | -15.62 | 1643   | .000             | -17.948         | 1.1490                | Lower: -20.201, Upper: -15.6943          |
| Equal variances not assumed       |        |      | -14.43 | 487.815| .000             | -17.948         | 1.2436                | Lower: -20.391, Upper: -15.5044          |

This section contains the results from the Independent Samples Test. The Levene's Test for Equality of Variances shows a significant F-value of 12.924 with a p-value of .000, indicating that the assumption of homogeneity of variance is not met.

The t-test for equality of means, assuming equal variances, shows a significant difference in means with a t-value of -15.62 and a p-value of .000. When equal variances are not assumed, the t-value is -14.43, also significant.

The 95% Confidence Interval for the mean difference ranges from -20.201 to -15.6943 when equal variances are assumed, and from -20.391 to -15.
Transcribed Image Text:### Analysis of Female Security Staff Percentages in Public and Private Prisons #### Group Statistics | Facility Type | N | Mean | Std. Deviation | Std. Error Mean | |---------------|-------|---------|----------------|-----------------| | Public | 1302 | 25.4351 | 18.34235 | 0.50833 | | Private | 343 | 43.3830 | 21.01978 | 1.13496 | This table displays the mean percentage of female security staff in public and private prison facilities. Public facilities show a mean of 25.44% with a standard deviation of 18.34, while private facilities have a mean of 43.38% with a standard deviation of 21.02. #### Independent Samples Test | Test | F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |-----------------------------------|--------|------|--------|--------|-----------------|-----------------|-----------------------|------------------------------------------| | Levene's Test for Equality of Variances | 12.924 | .000 | -15.62 | 1643 | .000 | -17.948 | 1.1490 | Lower: -20.201, Upper: -15.6943 | | Equal variances not assumed | | | -14.43 | 487.815| .000 | -17.948 | 1.2436 | Lower: -20.391, Upper: -15.5044 | This section contains the results from the Independent Samples Test. The Levene's Test for Equality of Variances shows a significant F-value of 12.924 with a p-value of .000, indicating that the assumption of homogeneity of variance is not met. The t-test for equality of means, assuming equal variances, shows a significant difference in means with a t-value of -15.62 and a p-value of .000. When equal variances are not assumed, the t-value is -14.43, also significant. The 95% Confidence Interval for the mean difference ranges from -20.201 to -15.6943 when equal variances are assumed, and from -20.391 to -15.
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