Group Statistics Std. Error Mean Age in Years N Mean Std. Deviation Math Achievement Lower than 13 553 50.6799 12.08868 51406 Higher than 14 443 50.9457 12.51362 59454 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference Significance Mean Difference Std. Error Difference Sig. df One-Sided p Two-Sided p Lower Upper Math Achievement Equal variances .770 381 -.340 994 367 734 -.26585 .78297 -1.80231 1.27061 assumed Equal variances not assumed - 338 932.565 .368 735 -26585 78596 -1.80831 1.27661 Independent Samples Effect Sizes 95% Confidence Interval Standardizer Point Estimate Lower Upper Math Achievement Cohen's d 12.27945 -.022 -147 .103 Hedges' correction 12.28873 -022 -147 .103 Glass's delta 12.51362 -.021 -146 .104 a. The denominator used in estimating the effect sizes. Cohen's d uses the pooled standard deviation. Hedges' correction uses the pooled standard deviation, plus a correction factor. Glass's delta uses the sample standard deviation of the control group.

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Is there a significant difference between age groups in math achievement?

**Group Statistics**

- **Math Achievement**

  | Age in Years      | N   | Mean   | Std. Deviation | Std. Error Mean |
  |-------------------|-----|--------|----------------|-----------------|
  | Lower than 13     | 553 | 50.6799 | 12.08868       | 0.51406         |
  | Higher than 14    | 443 | 50.9457 | 12.51362       | 0.59444         |

**Independent Samples Test**

- **Levene's Test for Equality of Variances**

  |                         | F    | Sig.   |
  |-------------------------|------|--------|
  | Math Achievement        | 0.770| 0.381  |

- **t-test for Equality of Means**

  |                         | t     | df     | Significance | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference |
  |                         |       |        | One-Sided p | Two-Sided p    |                       | Lower           | Upper           |
  |-------------------------|-------|--------|-------------|----------------|-----------------------|-----------------|-----------------|
  | Equal variances assumed | -0.340| 994    | 0.367       | 0.734          | -0.26585              | 0.78297         | -1.80231        | 1.27061        |
  | Equal variances not assumed | -0.338| 932.565 | 0.368   | 0.735          | -0.26585              | 0.78596         | -1.80831        | 1.27661        |

**Independent Samples Effect Sizes**

- **Math Achievement**

  | Standardizer          | Point Estimate | 95% Confidence Interval |
  |                       |                | Lower | Upper            |
  |-----------------------|----------------|-------|------------------|
  | **Cohen's d**         | 12.27945       | -0.022| 0.147 | 0.103     |
  | **Hedges' correction**| 12.28873       | -0.022| 0.147 | 0.103     |
  | **Glass's delta**     | 12.51362       | -0.021| 0
Transcribed Image Text:**Group Statistics** - **Math Achievement** | Age in Years | N | Mean | Std. Deviation | Std. Error Mean | |-------------------|-----|--------|----------------|-----------------| | Lower than 13 | 553 | 50.6799 | 12.08868 | 0.51406 | | Higher than 14 | 443 | 50.9457 | 12.51362 | 0.59444 | **Independent Samples Test** - **Levene's Test for Equality of Variances** | | F | Sig. | |-------------------------|------|--------| | Math Achievement | 0.770| 0.381 | - **t-test for Equality of Means** | | t | df | Significance | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | | | | | One-Sided p | Two-Sided p | | Lower | Upper | |-------------------------|-------|--------|-------------|----------------|-----------------------|-----------------|-----------------| | Equal variances assumed | -0.340| 994 | 0.367 | 0.734 | -0.26585 | 0.78297 | -1.80231 | 1.27061 | | Equal variances not assumed | -0.338| 932.565 | 0.368 | 0.735 | -0.26585 | 0.78596 | -1.80831 | 1.27661 | **Independent Samples Effect Sizes** - **Math Achievement** | Standardizer | Point Estimate | 95% Confidence Interval | | | | Lower | Upper | |-----------------------|----------------|-------|------------------| | **Cohen's d** | 12.27945 | -0.022| 0.147 | 0.103 | | **Hedges' correction**| 12.28873 | -0.022| 0.147 | 0.103 | | **Glass's delta** | 12.51362 | -0.021| 0
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