-What does it mean if two samples are significantly different from each other? What does it mean if they are not significantly different?-Economists say women make less than men in the United States by a wide margin. Do we find the same thing? What about income differences between White and Black Americans in the U.S.? How does our data fit with our understanding of pay discrepancies?in reference to t testsuse graph to answer questoins Group StatisticsRESPONDENTSStd. ErrorGENDERNMeanStd. DeviationMeanRespondent HouseholdIncome (in $)M47632372.3723710.0381086.748W50720793.8915915.295706.823Independent Samples TestLevene's Test for Equality ofVariancest-test for Equality of Means95% Confidence Interval of theDifferenceMeanStd. ErrorFSig.dfSig. (2-tailed)DifferenceDifferenceLowerUpperRespondent HouseholdIncome (in $)Equal variances54.564.0009.039981.00011578.4881280.9789064.71714092.260assumedEqual variances not8.931823.531.00011578.4881296.3879033.87614123.100assumedIndependent Samples Effect Sizes95% Confidence IntervalPointStandardizerEstimateLowerUpperRespondent HouseholdIncome (in $)Cohen's d20071.150.577.449.704Hedges'correction20086.511.576.449.704Glass's delta15915.295.728.594.860a. 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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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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Question

-What does it mean if two samples are significantly different from each other? What does it mean if they are not significantly different?

-Economists say women make less than men in the United States by a wide margin. Do we find the same thing? What about income differences between White and Black Americans in the U.S.? How does our data fit with our understanding of pay discrepancies?

in reference to t tests

use graph to answer questoins

Group Statistics
RESPONDENTS
Std. Error
GENDER
N
Mean
Std. Deviation
Mean
Respondent Household
Income (in $)
M
476
32372.37
23710.038
1086.748
W
507
20793.89
15915.295
706.823
Independent Samples Test
Levene's Test for Equality of
Variances
t-test for Equality of Means
95% Confidence Interval of the
Difference
Mean
Std. Error
F
Sig.
df
Sig. (2-tailed)
Difference
Difference
Lower
Upper
Respondent Household
Income (in $)
Equal variances
54.564
.000
9.039
981
.000
11578.488
1280.978
9064.717
14092.260
assumed
Equal variances not
8.931
823.531
.000
11578.488
1296.387
9033.876
14123.100
assumed
Independent Samples Effect Sizes
95% Confidence Interval
Point
Standardizer
Estimate
Lower
Upper
Respondent Household
Income (in $)
Cohen's d
20071.150
.577
.449
.704
Hedges'correction
20086.511
.576
.449
.704
Glass's delta
15915.295
.728
.594
.860
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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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