Statistics and analyzing data on an output

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statistical_and_developmental_studies_1.pdf

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Introduction to Statistics

Part A - Outputs:

1. A sample of university employees had been assembled. An output

concerning their education is presented below. Study the output and

answer the following questions:

a. What is the mean, median and the standard deviation?

b. Firstly, what is the interquartile range, and secondly, how many education years has

the most educated employee?

c. what is the number of education years that 36% of the sample has that number of

education years or below it? Answer the same question for 83%.

d. Firstly, how many employees has 12 education years or less? Secondly, how many

employees have missing values in the variable education years?

Statistics

Highest Year of School Completed

1510

12.88

12.00

2.984

8.904

19455

9.00

12.00

15.00

16.00

Valid

Missing

Mean

Median

Mode

St d. Dev iation

Variance

Range

Minimum

Maxim um

Sum

Percentiles

2. Researcher which studies the field of eating disorders checked the

correlation between subjects body image ranking and the degree to

which they restrict food intake. Study the output and answer the

following questions:

Highest Year of School Completed

2 .1 .1 .1

5 .3 .3 .5

5 .3 .3 .8

6 .4 .4 1.2

12 .8 .8 2.0

25 1.6 1.7 3.6

68 4.5 4.5 8.1

56 3.7 3.7 11.9

73 4.8 4.8 16.7

85 5.6 5.6 22.3

461 30.4 30.5 52.8

130 8.6 8.6 61.5

175 11.5 11.6 73.0

73 4.8 4.8 77.9

194 12.8 12.8 90.7

43 2.8 2.8 93.6

45 3.0 3.0 96.6

22 1.5 1.5 98.0

30 2.0 2.0 100.0

1510 99.5 100.0

7 .5

1517 100.0

Total

Valid

NAMissing

Total

Frequency Percent Valid Percent

Cumulat iv e

Percent

Correlati ons

1 .383**

.000

217 217

.383** 1

.000

217 217

Pearson Correlation

Sig. (2-tailed)

Pearson Correlation

Sig. (2-tailed)

Body perception

Restriction of f ood

intake (f asting)

Body

perception

Restriction of

f ood intake

(f asting)

Correlation is signif icant at the 0.01 lev el (2-t ailed).**.

1. What can be inferred from the table?

a. There is a significant negative correlation between the variables.

b. There is a moderately negative correlation between the variables.

c. There is a moderately positive correlation between the variables.

d. There is a weak positive correlation between the variables.

2. Report the correlation.

3. The following output present a regression done in order to predict

the number of SMS messages a person sends to his\hers partner by the

length of the relationship (in years). Study the output and answer the

following questions:

Regression

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 -.661(a) .436 .435 123.540

a Predictors: (Constant), Duration of relationship (years)

ANOVA(b)

Model Sum of Squares df Mean Square F Sig.

1 Regression 6010.000 1 100.000 365.381 .000(a)

Residual 7776.340 472 160.840

Total 13776.340 473

a Predictors: (Constant), Duration of relationship (years)

b Dependent Variable: SMS

Coefficients(a)

Model

Unstandardized

Coefficients

Standardized

Coefficients t Sig.

B Std. Error Beta B Std. Error

1 (Constant) 15.178 2821.912 -6.496 .000

Duration of relationship (years)

-0.183 204.547 .661 19.115 .000

a Dependent Variable: SMS

1. What is the percentage of explained variance?

2. Write the regression line equation.

3. Brad and Angelina are married for 25 years. According to this analysis, how many

SMS messages should Brad send Angelina?

4. A researcher is conducting a research on the effects of sociability on

mood. He is using a questionnaire in order to assess sociability. Study

the output concerning the reliability check and answer the following

questions:

Reliability

Scale: sociability

Case Processing Summary

N %

Cases

Valid 198 99.0

Excludeda 2 1.0

Total 200 100.0

a. Listwise deletion based on all variables in the

procedure.

Reliability Statistics

Cronbach's Alpha

Based on

Standardized Items

N of Items

.627 .659 8

Inter-Item Correlation Matrix

1 2 3 4 5 6 7 8

1. I like to see friends 1.000 .605 -.024 .189 .501 -.435 .451 .396

2. I talk a lot with friends on the phone .605 1.000 -.001 .362 .492 -.837 .509 .424

3. I like chocolate -.024 -.001 1.000 .003 .009 .001 -.001 -.017

4. I go to a lot of parties .189 .362 .003 1.000 .408 -.557 .430 .411

5. I have many friends .501 .492 .009 .408 1.000 -.243 .675 .510

6. I like to read alone at home -.435 -.837 .001 -.557 -.243 1.000 -.408 -.650

7. Romantic relationship are important .451 .509 -.001 .430 .675 -.408 1.000 .495

8. I feel good with my social status .396 .424 -.017 .411 .510 -.650 .495 1.000

Item-Total Statistics

Scale Mean if Item Deleted

Scale Variance if

Item Deleted

Corrected Item-

Total Correlation

Squared Multiple

Correlation

Cronbach's Alpha

if Item Deleted

1. I like to see friends 17.4495 26.188 .515 .443 .561

2. I talk a lot with friends on the phone

17.2374 24.009 .555 .472 .534

3. I like chocolate 16.1919 29.811 .007 .018 .686

4. I go to a lot of parties 15.9697 23.826 .399 .330 .571

5. I have many friends 16.7273 21.753 .666 .546 .489

6. I like to read alone at home 14.6768 35.540 -.320 .196 .753

7. Romantic relationship are important

17.0556 23.220 .634 .528 .512

8. I feel good with my social status

16.4192 23.260 .473 .397 .547

1. What is the number of subjects who's answers had been entered to the reliability

check?

2. What is the internal reliability of the sociability questionnaire?

3. which item (or items) would you suggest to change or omit (leave out)? explain why,

both from a statistical point of view and from the theoretical point of view.

Part B - statistical comprehension:

1. Study the table and answer the following questions:

Taken from Somer, E., Maguen, S., Or-Chen, K. & Litz, B. (2008). Managing Terror:

Differences between Jews and Arabs in Israel. International Journal of

Psychology, 42, 1-9.

Table 1

Demographic Variables of Jewish-Israelis and Arab-Israelis

Demographic

Characteristics

Jewish-

Israelis

(n = 100)

Arab-

Israelis

(n = 100)

Statistic comparing the

two groups

Age (years)

M = 43.60

(SD =

16.76)

M = 36.62

(SD=13.02)

t(198) = 10.82**

Gender

Male

Female

24%

76%

34%

66%

2 = 2.43

Marital status

Married

Non-Married

60%

40%

73%

27%

2 = 3.79

Religion

Jewish

Christian

Muslim

Druze

100%

72%

27%

2 = 200**

Table 1

Demographic Variables of Jewish-Israelis and Arab-Israelis

Demographic

Characteristics

Jewish-

Israelis

(n = 100)

Arab-

Israelis

(n = 100)

Statistic comparing the

two groups

Religiosity

Religious

laroitidarT

raluTra

%10

%26

%64

%18

%58

%24

2 = 32.66**

ecalphtriB

learaT

Other

%60

%40

%99

2 = 46.66**

*p<0.05

**p<0.01

1. What is the conclusion from the results of the test done between nationality and age ? Did a significant correlation had been found? Which test did the researchers use?

2. The Pearson correlation between all the of the research variables is displayed in the following table. Please report (in length) what is the most important correlation.

explain why.

Table 2

Correlations Among Variables in Regression Models

Variable 1 2 3 4 5 6 7 8 9 10

1. PTSD --

2. Depression .77** --

3. Somatization .58** .66** --

4. Group -.38** -.46 ** -.04 --

5. Age .03 -.03 .19** .23** --

6. Gender .21** .23** .20** .11 .05 --

7. Education -.22** -.23** -.27** .16* .06 -.05 --

8. Religiosity -.20** -.21** -.09 .34** .10 -.03 -.26** --

9. Marriage -.13 -.12 -.09 .14 -.47** -.04 .05 .15* --

10. Birthplace -.15 -.21** .02 .48** .45** .11 .08 .19** -.07 --

*p<0.05

**p<0.01

Good luck!