**Statistics Assessment **

**Social Research Skills 1**

In this assignment you will need a) to answer some general questions about quantitative data analysis and b) to answer some questions using data taken from the 2014 British Social Attitudes Survey. **All questions must be answered.**

**1. The following questions are about measurement **

List the different levels a variable may take and describe the properties of the levels.

Nominal level is where the variable only measures differences between cases such as gender. This is because nominal level does not need any ordering among its responses.

Ordinal level is where the variable can be ranked but the differences between categories is not available. An example can be educational achievement.

Interval level are numerical scales in which intervals have the same interpretation throughout, such as temperature, but it is unusual to see this used in social science.

Ratio level is an interval scale with the additional property that its zero position indicates the absence of the quantity being measured, such as income.

List the level of measurement that has been used for each of the variables in the dataset (other than the serial number)? Do not use the level of measurement in the data file. They have all been set to scale.

England, Scotland or Wales? – Nominal

Sex – Nominal

Age – Interval/ratio

Number of children in HH aged 4-15yrs – Interval/ratio

political party identification – Nominal

Better for govt to be formed of one party, or two in coalition? – Ordinal

How many, if any, cars or vans does your household own or have the regular use of? – Ordinal

How many trips did you make by plane during the last 12 months? – ordinal

How many employees do you supervise? – ordinal

How many hours do you normally work a week in your main job – including any paid or unpaid overtime? – Ordinal

Are you now a member of a trade union or staff association? – Ordinal

Do you tend to trust or tend not to trust the police? – ordinal

Respondent’s religion – nominal

How old were you when you completed your continuous full-time education? – Nominal

How important to always to vote in elections – ordinal

People who want children ought to get married – ordinal

Gay or lesbian couples should have the right to marry one another if they want to – ordinal

There is one law for the rich and one for the poor – ordinal

Left-right scale – ordinal

Libertarian-authoritarian scale – ordinal

Welfarism scale – ordinal

To which of these groups do you consider you belong? – ordinal

How important to help people in the rest of the world who are worse off than yourself: – ordinal

How do variables’ levels of measurement affect statistical analyses? Give examples.

Knowing the level of measure can help with how to interpret the data from that variable. This also means that the appropriate statistical analysis used on certain values because if the value was nominal then data would not be averaged or use a t-test on the data.

**2. You are required to report some descriptive statistics. Report your findings using any charts or tables you think are appropriate. **

**Report two measures of dispersion and two measures of central tendency of the number of children aged between 4 and 15 living in the respondents’ households?**

**Statistics**

Number of children in HH aged 4-15yrs dv

N

Valid

2878

Missing

0

Mean

.33

Median

.00

Mode

0

Std. Deviation

.741

Variance

.548

Range

5

Minimum

0

Maximum

5

Measures of central tendency were computed to summarize the data for the number of children in households aged 4-15yrs variable. Measures of dispersion were computed to understand the variability of scores for the number of children in households aged 4-15yrs variable. The following are the results of this analysis; N = 2878, M=0.33, SD=0.741. When you look at the mean, it appears that there is signficant number of children aged 4-15yrs living in households. Also, based on the small standard deviation, it looks like the data is not varied.

**What percentage of the sample believe it is better for government to be formed of one party on its own? (report valid percent) **

**Better for govt to be formed of one party, or two in coalition?**

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Gov’t formed by one political party on own

620

21.5

69.5

69.5

Gov’t formed by two political parties in coalition

272

9.5

30.5

100.0

Total

892

31.0

100.0

Missing

Not applicable

1907

66.3

Don’t know

76

2.6

Refused

3

.1

Total

1986

69.0

Total

2878

100.0

69.5% (valid percent) believe it is better for government to be formed of one party on its own.

**3. The following questions are about the number of employees respondents supervise . **

What is the greatest number of employees a respondent reported supervising?

**Statistics**

How many employees do you supervise? dv

N

Valid

2776

Missing

102

Maximum

3000

The greatest number of employees who responded to the report of supervising was 3000.

Recode the variable measuring how many employees respondents supervise into the following categories: 0 employees, 1- 10 employees, 11- 100 employees and more than 100 employees. Display the proportions in each category using appropriate tables and charts.

This bar chart shows that over 60% of respondents supervised were 0 employees, over 20% of respondents supervised were 1- 10 employees, near 10% of respondents supervised were 11-100 employees and near 5% of respondents supervised were over 100 employees.

What percentage of respondents who supervise 0 employees agree strongly there is one law for the rich and one for the poor?

25.1% respondents who supervise 0 employees agree strongly there is one law for the rich and one for the poor.

**4. The following question are about the age respondents were when they left education and their scores on a welfare scale. **

Report the confidence interval of the mean age respondents were when they left continuous full time education. Please give an interpretation of your results.

**One-Sample Test**

Test Value = 0

t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

Lower

Upper

How old were you when you completed your continuous full-time education?

90.416

2864

.000

19.053

18.64

19.47

We can be 95% confident that the mean on how old were you when you completed your continuous full-time education is between 18.64 and 19.47. This is significant due to significant value is less than the alpha value of 0.05, which means we can reject the null hypothesis.

Is respondents’ mean score on the scale measuring their attitudes to welfare significantly different from 3? Please give an interpretation of your results.

**One-Sample Test**

Test Value = 3

t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

Lower

Upper

Welfarism scale

-.479

2338

.632

-.0066929

-.034102

.020716

The mean is insignificant when testing at value of 3 so this means we cannot reject or accept the null hypothesis.

**5. The following question is about hypothesis testing and statistical significance. **

In your own words, define the concept of a sampling distribution.

Sampling distribution is where the possibility of obtaining each likely value of a statistic from a random sample of a population.

In your own words, describe the difference between a p value and an i??iˆ (alpha) value.

The alpha value is the probability of rejecting the null hypothesis when the null hypothesis is true whereas the p value is the probability of obtaining your sample data if the null hypothesis was true.

**6. The following questions are about behavioural and attitudinal differences between members of the sample. For each question you must select the appropriate test of significance, report relevant SPSS output and an interpretation of your results. **

a) Is respondents’ trust in the police independent of their race? Which test did you use and was it statistically significant?

**Do you tend to trust or tend not to trust the police? * To which of these groups do you consider you belong? Crosstabulation**

Count

To which of these groups do you consider you belong?

Total

Black

Asian

White

Do you tend to trust or tend not to trust the police?

Trust it a great deal

6

23

239

268

Tend to trust it

32

48

1124

1204

Tend to distrust it

22

10

246

278

Distrust it greatly

5

1

94

100

Total

65

82

1703

1850

I used the Chi-squared test on the data. You could argue that the data does show that the respondents trust in the police may not be independent of their race, however I do not believe this was statistically significant due to needing a larger sample size to being to prove or disprove this hypothesis.

How does the mean rating respondents give to helping people in the rest of the world who are worse off than you differ by religion? Which test did you use and was it statistically significant?

**Ranks**

Respondent’s religion

dv

N

Mean Rank

How important to help people in the rest of the world who are worse off than yourself: [S-C]AC

Church of England/Anglican

286

305.02

Roman Catholic

154

389.22

Other Christian

247

360.93

Total

687

**Ranks**

How important to help people in the rest of the world who are worse off than yourself: [S-C]AC

N

Mean Rank

Respondent’s religion

dv

Not at all important

133

227.30

2

135

236.29

3

178

210.96

Total

446

I used the Kruskal Wallis test. You could argue that the data does show religion has a higher mean rank then to how important to help people in the rest of the world who are worse off than yourself. This is not statistically significant as it does prove or reject the null hypothesis.

Describe the association between the numbers of cars and vans people own or have regular use of and the number of trips they can make by plane during the last 12 months? Which test did you use and was it statistically significant?

**Correlations**

How many, if any, cars or vans does your household own or have the regular use of?

How many trips did you make by plane during the last 12 months?

How many, if any, cars or vans does your household own or have the regular use of?

Pearson Correlation

1

.502^{**}

Sig. (2-tailed)

.000

N

2878

2878

How many trips did you make by plane during the last 12 months?

Pearson Correlation

.502^{**}

1

Sig. (2-tailed)

.000

N

2878

2878

**. Correlation is significant at the 0.01 level (2-tailed).

I used the Pearsons Correlation Coefficient test. It was statistically significant because there is no correlation between the variables.

How does the mean age respondents left full-time education differ across men and women? Which test did you use and was it statistically significant?

**How old were you when you completed your continuous full-time education? * Person 1 SEX Crosstabulation**

Person 1 SEX

Total

Male

Female

How old were you when you completed your continuous full-time education?

1

1

0

1

4

0

1

1

10

1

0

1

11

2

1

3

12

1

3

4

13

0

4

4

14

67

67

134

15

247

327

574

16

374

438

812

17

86

130

216

18

116

208

324

19

29

48

77

20

31

42

73

21

102

127

229

22

72

87

159

23

36

48

84

24

23

22

45

25

14

8

22

26

13

7

20

27

3

2

5

28

6

1

7

29

2

2

4

30

1

4

5

31

1

1

2

34

1

0

1

35

1

0

1

38

0

1

1

95

0

3

3

96

21

26

47

97

2

4

6

Total

1253

1612

2865

I used the Chi-squared test on the data. There is not much difference males and females in regards to what age they left education so this statistic test was statistically insignificant.

**7. The following questions are about modelling the relationship between belief in always voting in elections and respondents’ age. Please include all relevant SPSS output and interpret your results. **

a) Model respondents’ beliefs about the importance of always voting in elections as a function of their age. What is the expected change in the scores measuring respondents’ beliefs in the importance of voting with a unit change in their age?

**Person 1 age last birthday * How important to always to vote in elections: [S-C]AC Crosstabulation**

Count

How important to always to vote in elections: [S-C]AC

Total

Not at all important

2

3

4

5

6

“Very important”

Person 1 age last birthday

18

2

1

2

2

2

1

3

13

19

1

0

0

1

3

2

5

12

20

1

1

2

2

1

3

2

12

21

2

1

2

2

3

1

2

13

22

2

1

0

1

2

1

7

14

23

4

2

0

0

2

4

4

16

24

2

1

3

5

4

2

0

17

25

1

2

5

1

1

2

6

18

26

3

1

1

2

4

1

4

16

27

1

1

0

4

2

6

8

22

28

3

1

0

4

7

1

9

25

29

1

0

2

1

2

1

6

13

30

1

1

4

4

4

2

5

21

31

2

1

3

2

1

5

7

21

32

2

0

2

2

2

3

6

17

33

2

0

1

1

2

1

7

14

34

0

0

1

3

0

3

7

14

35

1

4

1

2

1

5

15

29

36

1

0

6

2

3

5

12

29

37

1

0

1

2

3

5

6

18

38

1

0

3

1

0

3

13

21

39

1

0

3

4

6

0

9

23

40

1

0

2

3

6

1

8

21

41

3

1

4

7

6

3

12

36

42

4

2

4

6

3

3

14

36

43

1

3

1

4

5

4

14

32

44

1

0

0

3

0

1

8

13

45

1

1

6

1

4

3

12

28

46

4

0

1

3

2

2

14

26

47

2

1

1

0

3

2

14

23

48

2

2

0

3

3

4

8

22

49

3

0

0

3

6

7

10

29

50

2

0

4

1

1