Whether Men and Women Differ in Their Mean Socioeconomic Index - Statistics Project Example

I do not see any problem with doing a t-test.

Descriptives

 

RESPONDENTS SEX

Statistic

Std. Error

RESPONDENT SOCIOECONOMIC INDEX

MALE

Mean

49.109

.6527

95% Confidence Interval for Mean

Lower Bound

47.828

 

Upper Bound

50.390

 

5% Trimmed Mean

48.238

 

Median

42.200

 

Variance

377.909

 

Std. Deviation

19.4399

 

Minimum

17.1

 

Maximum

97.2

 

Range

80.1

 

Interquartile Range

32.0

 

Skewness

.543

.082

Kurtosis

-.981

.164

FEMALE

Mean

48.458

.6115

95% Confidence Interval for Mean

Lower Bound

47.258

 

Upper Bound

49.658

 

5% Trimmed Mean

47.834

 

Median

38.900

 

Variance

382.894

 

Std. Deviation

19.5677

 

Minimum

17.1

 

Maximum

97.2

 

Range

80.1

 

Interquartile Range

31.5

 

Skewness

.501

.076

Kurtosis

-1.055

.153

 

The box plots presented below show little or no difference in the socio-economic index of the male and female participants.

 

 

 

1. Age when their first child was born (agekdbrn)

The standard error for the male participants is given as 0.218 while that of female participants is given as 0.174; this shows a big difference in the age of the father when their first child was born for the male and the female participants. I do not see any problem with doing a t-test.

 

Descriptives

 

RESPONDENTS SEX

Statistic

Std. Error

R'S AGE WHEN 1ST CHILD BORN

MALE

Mean

25.00

.218

95% Confidence Interval for Mean

Lower Bound

24.57

 

Upper Bound

25.43

 

5% Trimmed Mean

24.73

 

Median

24.00

 

Variance

29.635

 

Std. Deviation

5.444

 

Minimum

14

 

Maximum

46

 

Range

32

 

Interquartile Range

7

 

Skewness

.790

.098

Kurtosis

.635

.195

FEMALE

Mean

22.87

.174

95% Confidence Interval for Mean

Lower Bound

22.53

 

Upper Bound

23.21

 

5% Trimmed Mean

22.57

 

Median

21.00

 

Variance

26.292

 

Std. Deviation

5.128

 

Minimum

13

 

Maximum

44

 

Range

31

 

Interquartile Range

7

 

Skewness

.888

.083

Kurtosis

.485

.166

 

The box plots presented below show little or no difference in the age of the father when their first child was born for the male and the female participants.

 

 

 

2. Now do a t-test for each variable, by gender. Is the homogeneity of variance assumption met, or not? What do you conclude about mean differences by gender?

SOLUTION

1. Mean socioeconomic index (sei)

The table below gives the t-test. It is clear that the homogeneity of variance assumption is met since the p-value for Levene’s test is greater than α=0.05. It is therefore evident that the variability in the male and female participants is the same. 

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

RESPONDENT SOCIOECONOMIC INDEX

Equal variances assumed

.256

.613

.728

1909

.467

.6515

.8948

-1.1034

2.4065

Equal variances not assumed

 

 

.728

1874

.466

.6515

.8944

-1.1026

2.4057

 

In regard to mean differences by gender, we see that there is no significant difference in the socio-economic index of the two genders (male and female) since the p-value is greater than α=0.05 we fail to reject the null hypothesis.

1. Age when their first child was born (agekdbrn)

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

R'S AGE WHEN 1ST CHILD BORN

Equal variances assumed

.724

.395

7.704

1000

.000

2.130

.276

1.588

2.672

Equal variances not assumed

 

 

7.629

 

.000

2.130

.279

1.582

2.677

The table above gives the t-test. It is clear that the homogeneity of variance assumption is met since the p-value for Levene’s test is greater than α=0.05. It is therefore evident that the variability in the male and female participants is the same. 

In regard to mean differences by gender, we see that there is no significant difference in the socio-economic index of the two genders (male and female) since the p-value is greater than α=0.05 we fail to reject the null hypothesis.

3. Create an error bar chart for each variable by gender. Is the graph consistent with the result from the t-test?

SOLUTION

1. Mean socioeconomic index (sei)

The figure below represents the error bar chart for the respondents’ socio-economic index based on gender. We can clearly see a significant difference in the mean socioeconomic index for males and for females. The graph is therefore consistent with the result from the t-test

 

1. Age when their first child was born (agekdbrn

The figure below represents the error bar chart for the respondents’ age of the father when their first child was born. We can clearly see a significant difference in the mean age of the father when their first child was born for males and for females. The graph is therefore consistent with the result from the t-test

 

PART TWO

1. One variable in the customer survey asked about the agreement that SPSS products are a good value (value). A second question asked about the agreement that SPSS offers high-quality products (hiqualty). Use a paired-samples t-test to see whether the means of these two questions differ (they are measured on a five-point scale). What do you conclude?

SOLUTION

 

Paired Samples Statistics

 

 

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

SPSS prods are a gd val

2.66

890

1.055

.035

SPSS offers high-quality prods

2.08

890

.793

.027

 

 

Paired Samples Correlations

 

 

N

Correlation

Sig.

Pair 1

SPSS prods are a gd Val & SPSS offers high-quality prods

890

.451

.000

 

 

Paired Samples Test

 

 

Paired Differences

t

df

Sig. (2-tailed)

 

 

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

 

 

Lower

Upper

Pair 1

SPSS prods are a gd Val - SPSS offers high-quality prods

.579

.993

.033

.513

.644

17.381

889

.000

 

From the above tables, we observe the p-value to be 0.000 (a value less than α=0.05), we, therefore, reject the null hypothesis and conclude that indeed the means of these two questions are different at a 5% significance level.

2. Then test whether there is a meaningful difference between an agreement that SPSS products are easy to learn (easylrn) and SPSS products are easy to use (easyuse). What do you conclude?

SOLUTION

 

Paired Samples Statistics

 

 

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

SPSS prods are easy to learn

2.62

900

1.050

.035

SPSS prods are easy to use

2.63

900

1.050

.035

 

 

Paired Samples Correlations

 

 

N

Correlation

Sig.

Pair 1

SPSS prods are easy to learn & SPSS prods are easy to use

900

.811

.000

 

 

Paired Samples Test

 

 

Paired Differences

t

df

Sig. (2-tailed)

 

 

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

 

 

Lower

Upper

Pair 1

SPSS prods are easy to learn - SPSS prods are easy to use

-.006

.646

.022

-.048

.037

-.258

899

.796

 

From the above tables, we observe the p-value to be 0.796 (a value greater than α=0.05), we, therefore, fail to reject the null hypothesis and conclude the mean agreement that SPSS products are easy to learn (easylrn) and SPSS products are easy to use (easyuse) are same at 5% significance level.

3. Could we use a paired-sample t-test to compare how long a customer has used SPSS products (usespss) and how frequently they use SPSS (freqspss)? Why or why not?

SOLUTION

No, we can’t use a paired-sample t-test; the reason for not using a paired-sample t-test I that the two variables have different scale measurements.

 

PART THREE

1. Investigate how the number of siblings (sibs) varies by highest degree (degree). Ask for appropriate statistics.

SOLUTION

The p-value is given as 0.000 (a value less than α=0.05), we, therefore, reject the null hypothesis and conclude that there is an association between the number of siblings and the highest degree. Those with much higher degrees have fewer siblings.

 

ANOVA

NUMBER OF BROTHERS AND SISTERS

 

 

 

 

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

2106.493

4

526.623

57.653

.000

Within Groups

18405.814

2015

9.134

 

 

Total

20512.307

2019

 

 

 

 

 

2. Is the assumption of homogeneity of variance met? Is the ANOVA test significant at the .01 level?

SOLUTION

It is clear that the homogeneity of variance assumption is not met since the p-value for Levene’s test is less than α=0.05. It is therefore evident that the variability in the number of siblings and the highest degree of participants is not the same. 

 

Test of Homogeneity of Variances

NUMBER OF BROTHERS AND SISTERS

Levene Statistic

df1

df2

Sig.

31.134

4

2015

.000

 

The p-value for the F-test is 0.000 (a value less than α=0.05), we, therefore, reject the null hypothesis and conclude the ANOVA test is significant at the .01 level

3. Do a post hoc analysis, if justified. Ask for both the Bonferroni and Scheffe tests. What do you conclude from these tests? Which education groups have different mean numbers of children? Are the Bonferroni and Scheffe tests consistent?

SOLUTION

From the post hoc test, we can conclude that there are variables that are significantly different from each other.

 

Multiple Comparisons

Dependent Variable: NUMBER OF BROTHERS AND SISTERS

 

 

 

 

 

 

(I) RS HIGHEST DEGREE

(J) RS HIGHEST DEGREE

Mean Difference (I-J)

Std. Error

Sig.

95% Confidence Interval

 

Lower Bound

Upper Bound

Scheffe

Less than primary/high school

Primary/High School

1.969*

.200

.000

1.35

2.58

Post Primary/High School

2.346*

.289

.000

1.45

3.24

BACHELOR

3.261*

.238

.000

2.53

3.99

GRADUATE

3.330*

.279

.000

2.47

4.19

Primary/High School

Less than primary/high school

-1.969*

.200

.000

-2.58

-1.35

Post Primary/High School

.377

.249

.682

-.39

1.14

BACHELOR

1.292*

.187

.000

.72

1.87

GRADUATE

1.362*

.237

.000

.63

2.09

Post Primary/High School

Less than primary/high school

-2.346*

.289

.000

-3.24

-1.45

Primary/High School

-.377

.249

.682

-1.14

.39

BACHELOR

.915*

.280

.031

.05

1.78

GRADUATE

.985*

.316

.046

.01

1.96

BACHELOR

Less than primary/high school

-3.261*

.238

.000

-3.99

-2.53

Primary/High School

-1.292*

.187

.000

-1.87

-.72

Post Primary/High School

-.915*

.280

.031

-1.78

-.05

GRADUATE

.069

.270

.999

-.76

.90

GRADUATE

Less than primary/high school

-3.330*

.279

.000

-4.19

-2.47

Primary/High School

-1.362*

.237

.000

-2.09

-.63

Post Primary/High School

-.985*

.316

.046

-1.96

-.01

BACHELOR

-.069

.270

.999

-.90

.76

Bonferroni

Less than primary/high school

Primary/High School

1.969*

.200

.000

1.41

2.53

Post Primary/High School

2.346*

.289

.000

1.53

3.16

BACHELOR

3.261*

.238

.000

2.59

3.93

GRADUATE

3.330*

.279

.000

2.55

4.11

Primary/High School

Less than primary/high school

-1.969*

.200

.000

-2.53

-1.41

Post Primary/High School

.377

.249

1.000

-.32

1.08

BACHELOR

1.292*

.187

.000

.77

1.82

GRADUATE

1.362*

.237

.000

.70

2.03

Post Primary/High School

Less than primary/high school

-2.346*

.289

.000

-3.16

-1.53

Primary/High School

-.377

.249

1.000

-1.08

.32

BACHELOR

.915*

.280

.011

.13

1.70

GRADUATE

.985*

.316

.019

.10

1.87

BACHELOR

Less than primary/high school

-3.261*

.238

.000

-3.93

-2.59

Primary/High School

-1.292*

.187

.000

-1.82

-.77

Post Primary/High School

-.915*

.280

.011

-1.70

-.13

GRADUATE

.069

.270

1.000

-.69

.83

GRADUATE

Less than primary/high school

-3.330*

.279

.000

-4.11

-2.55

Primary/High School

-1.362*

.237

.000

-2.03

-.70

Post Primary/High School

-.985*

.316

.019

-1.87

-.10

BACHELOR

-.069

.270

1.000

-.83

.69

*. The mean difference is significant at the 0.05 level.

 

 

 

 

 

 

 

 

NUMBER OF BROTHERS AND SISTERS

 

RS HIGHEST DEGREE

N

Subset for alpha = 0.05

 

1

2

3

Scheffea

GRADUATE

194

2.40

 

 

BACHELOR

354

2.47

 

 

Post Primary/High School

173

 

3.38

 

Primary/High School

1002

 

3.76

 

Less than primary/high school

297

 

 

5.73

Sig.

 

.999

.709

1.000

Means for groups in homogeneous subsets are displayed.

 

a. Uses Harmonic Mean Sample Size = 275.864.

 

 

 

 

 

 

 

 

 

 

 

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