T-Test Independent Samples Test Levene\'s Test for Equality of Variances t-test

Question

T-Test

Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

CompassR

Equal variances assumed

2.181

.141

-1.831

235

.068

-.167

.091

-.346

.013

Equal variances not assumed

-1.860

230.031

.064

-.167

.090

-.344

.010

ReligionR

Equal variances assumed

3.140

.078

2.871

236

.004

.468

.163

.147

.789

Equal variances not assumed

2.919

232.460

.004

.468

.160

.152

.783

WomanR

Equal variances assumed

1.435

.232

-.767

236

.444

-.114

.149

-.407

.179

Equal variances not assumed

-.751

200.966

.453

-.114

.152

-.414

.185

Among many other issues, Juddi Trent is interested in whether or not there are sex differences in voters’ perceptions of the ideal presidential candidate. On the following page, there is an output concerning sex differences on three of these characteristics or issues: (1); it is important that the candidate is compassionate about the needs of people; (2) It is important that the candidate talk about his/her personal religious beliefs, and (3) it is important that the country elect a woman as president or vice president.

The following table describes her hypotheses.

Item

Hypothesis

It is important that the candidate is compassionate about the needs of people [CompassR]

Women > Men

It is important that the candidate talk about his/her personal religious beliefs [ReligionR]

Not sure

It is important that the country elect a woman as president or vice president [WomanR]

Women > Men

Results relevant to these three items are reproduced on the next page. For each characteristic or issue, answer the following questions (i.e., provide three answers to each question). Assume an of .05

In each case, which group found each characteristic more important?

Compass:

Religion:

Women:

In each case, is the difference between groups (i.e., men and women) statistically significant? How do you know?

Compass:

Religion:

Women:

In each case, what do you conclude about the null hypothesis?

Compass:

Religion:

Women:

In each case, compute 2. Is each result small, medium, or large? SHOW YOUR WORK.

Compass:

Religion:

Women:

Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

CompassR

Equal variances assumed

2.181

.141

-1.831

235

.068

-.167

.091

-.346

.013

Equal variances not assumed

-1.860

230.031

.064

-.167

.090

-.344

.010

ReligionR

Equal variances assumed

3.140

.078

2.871

236

.004

.468

.163

.147

.789

Equal variances not assumed

2.919

232.460

.004

.468

.160

.152

.783

WomanR

Equal variances assumed

1.435

.232

-.767

236

.444

-.114

.149

-.407

.179

Equal variances not assumed

-.751

200.966

.453

-.114

.152

-.414

.185

Explanation / Answer

let first sample is of women and second sample is of men then

mean difference = women -men

taking the consideration of equal variances

(first) In each case, which group found each characteristic more important?

Compass:men ( since mean difference is negative)

Religion:women(since mean difference is positive)

Women:women(since mean difference is positive)

In each case, is the difference between groups (i.e., men and women) statistically significant? How do you know?

Compass: statistically significant as one tailed p-value=0.068/2=0.034 is less than alpha=0.05

here alternate hypothesis is one tailed(women>men)

Religion:statistically significant as two tailed p-value=0.004 is less than alpha=0.05

here alternate hypothesis is two tailed(here women>men or women<men or women=men )

Women:statistically not significant as one tailed p-value=0.444/2=0.222 is more than alpha=0.05

here alternate hypothesis is one tailed(women>men)

In each case, what do you conclude about the null hypothesis?

Compass: Reject null hypothesisH0

Religion:Reject null hypothesisH0

Women: donot reject null hypothesis

In each case, compute 2. Is each result small, medium, or large? SHOW YOUR WORK.

2=t2/(t2+n1+n2-2), n1+n2-2 is df of corresponding t-test

Compass:2=(-1.831)*(-1.831)/((-1.831)*(-1.831)+235)=0.0141

Religion::2=(2.871)*(2.871)/((2.871)*(2.871)+236)=0.0337

Women::2=(-0.767)*(-0.767)/((-0.767)*(-0.767)+235)=0.0025

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