Part 1 Differences between two means (T test) Differences in sleep and income by sex Group Statistics Sex N Mean Std Deviation Std Error Mean Weight in pounds Male 170 168 12 24 210 1 857 Female 136 129 51 18 429 1 580 Average hours of sleep per night Male 170 7 653 1 5981 1226 Female 136 8 281 1 8569 1592 Household income Male 170 39403 24 19235 298 1475 280 Female 136 41150 75 19850 689 1702 183 Independent Samples Effect Sizes Standardizer a Point Estimate 95 Confidence Interval Lower Upper Weight in pounds Cohen's d 21 832 1 769 1 502 2 033 Hedges' correction 21 886 1 764 1 498 2 028 Glass's delta 18 429 2 095 1 757 2 430 Average hours of sleep per night Cohen's d 1 7178 366 593 138 Hedges' correction 1 7221 365 591 138 Glass's delta 1 8569 338 567 109 Household income Cohen's d 19510 976 090 315 136 Hedges' correction 19559 277 089 314 136 Glass's delta 19850 689 088 314 138 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 Part 1 Differences between two means Review your data output from your T tests 1 If we use t tests to assess a significant difference between two means, why do we have consider the variance of the two group scores as part of this process (1 mark) 2 Did you violate assumptions of variance with any of the t tests Explain (2 marks) 3 What would be the statistical conclusion from the analyses for both sleep, income and weight Ensure that in your conclusion you express your t scores from your data (see Powerpoint and T test Practice assignment for how to express t values for such write ups) (2 marks) 4 You ran three t tests in this experiment Why is this not advised (1 mark) 5 Which type of t test (dependent or independent) will always have less pooled variance associated with it Why (2 marks) 6 Why does the t distribution use standard error instead of the standard deviation z scores (2 marks) Weight in pounds Average hours of sleep per night Household income Equal variances assumed Equal variances not assumed Equal variances assumed Equal variances not assumed Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances Sig F Independent Samples Test t df 304 15 375 15 838 303 291 3 178 304 3 126 267 387 779 304 776 285 365 9 279 456 260 003 500 610 Sig (2 tailed)

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Part 1 Differences between two means (T-test) Differences in sleep and income by sex Group Statistics Sex N Mean Std. Deviation Std. Error Mean Weight

Part 1 Differences between two means (T-test)

‘Differences in sleep and income by sex’ Group Statistics
	Sex	N	Mean	Std. Deviation	Std. Error Mean
Weight in pounds	Male	170	168.12	24.210	1.857
Weight in pounds	Female	136	129.51	18.429	1.580
Average hours of sleep per night	Male	170	7.653	1.5981	.1226
Average hours of sleep per night	Female	136	8.281	1.8569	.1592
Household income	Male	170	39403.24	19235.298	1475.280
Household income	Female	136	41150.75	19850.689	1702.183

Independent Samples Effect Sizes
		Standardizer^a	Point Estimate	95% Confidence Interval
		Standardizer^a	Point Estimate	Lower	Upper
Weight in pounds	Cohen's d	21.832	1.769	1.502	2.033
	Hedges' correction	21.886	1.764	1.498	2.028
	Glass's delta	18.429	2.095	1.757	2.430
Average hours of sleep per night	Cohen's d	1.7178	-.366	-.593	-.138
	Hedges' correction	1.7221	-.365	-.591	-.138
	Glass's delta	1.8569	-.338	-.567	-.109
Household income	Cohen's d	19510.976	-.090	-.315	.136
	Hedges' correction	19559.277	-.089	-.314	.136
	Glass's delta	19850.689	-.088	-.314	.138
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. Part 1 Differences between two means Review your data output from your T-tests. 1. If we use t-tests to assess a significant difference between two means, why do we have consider the variance of the two group scores as part of this process? (1 mark) 2. Did you violate assumptions of variance with any of the t-tests? Explain. (2 marks) 3. What would be the statistical conclusion from the analyses for both sleep, income and weight? Ensure that in your conclusion you express your t-scores from your data (see Powerpoint and T-test Practice assignment for how to express t-values for such write-ups) (2 marks) 4. You ran three t-tests in this experiment. Why is this not advised? (1 mark) 5. Which type of t-test (dependent or independent) will always have less pooled variance associated with it? Why? (2 marks) 6. Why does the t-distribution use standard error instead of the standard deviation/z-scores? (2 marks)

Weight in pounds Average hours of sleep per night Household income. Equal variances assumed Equal variances not assumed Equal variances assumed Equal variances not assumed. Equal variances assumed Equal variances not. assumed. Levene's Test for Equality of Variances Sig. F Independent Samples Test t df 304 15.375 15.838 303.291 -3.178 304 -3.126 267.387 -.779 304 -.776 285.365 9.279 .456 .260 .003 .500 .610 Sig. (2-tailed)

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