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Paired Samples Statistics Std. Error Mean N Std. Deviation Mean Pair 1 Errors after 8 hours sleep deprivation 6.75 20 2.124 475 Errors after 24 hours 13.90 20 2.024 452 sleep deprivation Paired Samples Correlations Significance Correlation One-Sided p Two-Sided p Pair 1 Errors after 8 hours sleep deprivation & Errors after 24 hours sleep deprivation 20 -.263 .131 262 Paired Samples Test Paired Differences Significance 95% Confidence Interval of the Difference Std. Error Mean Std. Deviation Mean Lower Upper df One-Sided p Two-Sided p Pair 1 Errors after 8 hours sleep deprivation - Errors after 24 hours sleep deprivation -7.150 3.297 .737 -8.693 -5.607 -9.698 19 <.001 <.001 Paired Samples Effect Sizes 95% Confidence Interval Point Standardizer Estimate Lower Upper Cohen's d Pair 1 Errors after 8 hours sleep deprivation - Errors after 24 hours sleep deprivation 3.297 -2.169 -2.972 -1.348 Hedges' correction 3.364 -2.125 -2.913 -1.321 a. The denominator used in estimating the effect sizes. Cohen's d uses the sample standard deviation of the mean difference. Hedges' correction uses the sample standard deviation of the mean difference, plus a correction factor.

Paired Samples Statistics Std. Error Mean N Std. Deviation Mean Pair 1 Errors after 8 hours sleep deprivation 6.75 20 2.124 475 Errors after 24 hours 13.90 20 2.024 452 sleep deprivation Paired Samples Correlations Significance Correlation One-Sided p Two-Sided p Pair 1 Errors after 8 hours sleep deprivation & Errors after 24 hours sleep deprivation 20 -.263 .131 262 Paired Samples Test Paired Differences Significance 95% Confidence Interval of the Difference Std. Error Mean Std. Deviation Mean Lower Upper df One-Sided p Two-Sided p Pair 1 Errors after 8 hours sleep deprivation - Errors after 24 hours sleep deprivation -7.150 3.297 .737 -8.693 -5.607 -9.698 19 <.001 <.001 Paired Samples Effect Sizes 95% Confidence Interval Point Standardizer Estimate Lower Upper Cohen's d Pair 1 Errors after 8 hours sleep deprivation - Errors after 24 hours sleep deprivation 3.297 -2.169 -2.972 -1.348 Hedges' correction 3.364 -2.125 -2.913 -1.321 a. The denominator used in estimating the effect sizes. Cohen's d uses the sample standard deviation of the mean difference. Hedges' correction uses the sample standard deviation of the mean difference, plus a correction factor.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Paired Samples Statistics - **Pair 1 Statistics:** - **Errors after 8 hours sleep deprivation:** - Mean: 6.75 - N (Sample Size): 20 - Standard Deviation (Std. Deviation): 2.124 - Standard Error of the Mean (Std. Error Mean): 0.475 - **Errors after 24 hours sleep deprivation:** - Mean: 13.90 - N (Sample Size): 20 - Standard Deviation (Std. Deviation): 2.024 - Standard Error of the Mean (Std. Error Mean): 0.452 ### Paired Samples Correlations - **Pair 1 Correlation:** - Errors after 8 hours vs. Errors after 24 hours - N (Sample Size): 20 - Correlation: -0.263 - Significance: - One-Sided p: 0.131 - Two-Sided p: 0.262 ### Paired Samples Test - **Pair 1 Difference:** - Errors after 8 hours - Errors after 24 hours - Mean Difference: -7.150 - Standard Deviation: 3.297 - Standard Error of the Mean Difference: 0.737 - 95% Confidence Interval of the Difference: - Lower: -8.693 - Upper: -5.607 - t-value: -9.698 - Degrees of Freedom (df): 19 - Significance: - One-Sided p: <0.001 - Two-Sided p: <0.001 ### Paired Samples Effect Sizes - **Pair 1 Effect Size:** - Errors after 8 hours - Errors after 24 hours - Cohen's d: - Standardizer: 3.297 - Point Estimate: -2.169 - 95% Confidence Interval: - Lower: -2.972 - Upper: -1.348 - Hedges' correction: - Standardizer: 3.364 - Point Estimate: -2.125 - 95% Confidence Interval: - Lower: -2.913 - Upper: -1.321
Transcribed Image Text:### Paired Samples Statistics - **Pair 1 Statistics:** - **Errors after 8 hours sleep deprivation:** - Mean: 6.75 - N (Sample Size): 20 - Standard Deviation (Std. Deviation): 2.124 - Standard Error of the Mean (Std. Error Mean): 0.475 - **Errors after 24 hours sleep deprivation:** - Mean: 13.90 - N (Sample Size): 20 - Standard Deviation (Std. Deviation): 2.024 - Standard Error of the Mean (Std. Error Mean): 0.452 ### Paired Samples Correlations - **Pair 1 Correlation:** - Errors after 8 hours vs. Errors after 24 hours - N (Sample Size): 20 - Correlation: -0.263 - Significance: - One-Sided p: 0.131 - Two-Sided p: 0.262 ### Paired Samples Test - **Pair 1 Difference:** - Errors after 8 hours - Errors after 24 hours - Mean Difference: -7.150 - Standard Deviation: 3.297 - Standard Error of the Mean Difference: 0.737 - 95% Confidence Interval of the Difference: - Lower: -8.693 - Upper: -5.607 - t-value: -9.698 - Degrees of Freedom (df): 19 - Significance: - One-Sided p: <0.001 - Two-Sided p: <0.001 ### Paired Samples Effect Sizes - **Pair 1 Effect Size:** - Errors after 8 hours - Errors after 24 hours - Cohen's d: - Standardizer: 3.297 - Point Estimate: -2.169 - 95% Confidence Interval: - Lower: -2.972 - Upper: -1.348 - Hedges' correction: - Standardizer: 3.364 - Point Estimate: -2.125 - 95% Confidence Interval: - Lower: -2.913 - Upper: -1.321
**Levene's Test of Equality of Variances** Levene's test evaluates whether the variances of two or more groups are equal. Below are the options for interpreting the results of Levene’s test: - \( \circ \) The result is significant, so the variances are equal. - \( \circ \) The result is significant, so the variances are unequal. - \( \circ \) The result is nonsignificant, so the variances are equal. - \( \circ \) The result is nonsignificant, so the variances are unequal. - \( \circ \) None of the above Understanding how to interpret the test results correctly is crucial for statistical analysis. Typically, a significant result indicates that variances are unequal, while a nonsignificant result suggests that variances are equal.
Transcribed Image Text:**Levene's Test of Equality of Variances** Levene's test evaluates whether the variances of two or more groups are equal. Below are the options for interpreting the results of Levene’s test: - \( \circ \) The result is significant, so the variances are equal. - \( \circ \) The result is significant, so the variances are unequal. - \( \circ \) The result is nonsignificant, so the variances are equal. - \( \circ \) The result is nonsignificant, so the variances are unequal. - \( \circ \) None of the above Understanding how to interpret the test results correctly is crucial for statistical analysis. Typically, a significant result indicates that variances are unequal, while a nonsignificant result suggests that variances are equal.
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Step 1

If we want to compare 2(+) groups on a quantitative variable, we usually want to know if they have equal mean scores. For finding out if that's the case, we often use

  • an independent sample t test for 2 groups or
  • a one-way ANOVA  for 3+ groups.

Both tests require the homogeneity assumption: the population variances of the dependent variable must equal for all groups. You can ignore this assumption if you have roughly equal sample sizes for each group. However, if you have sharply different sample sizes, then you do need to make sure that homogeneity of variances is met by your data.

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