Assignment SPSS Word2

SPSS Assignment Answers to Questions Question 1.

(a). The scatter plot of the two variables that are variable crate and variable variable educat treating crime rate as dependent variable is shown below. [ file from crime.sav]

(b). after superimposing a straight line on to the scatter plot that is using the linear fit method, the relationship roughly looks linear R sq linear of .066. Although it may be curving up slightly or there may be an outlier. But if we use the cubic fit method the values are more fitted because the value of R [.242] for the cubic fit method is higher than the linear fit.

Msc program in Energy Technology, Mechanical Engineering

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SPSS Assignment

(c) From the Pearson’s correlation value we can say that, there is a perfect positive correlation between these variables, which is statically significant at the 5% level. Because the perason’s coefficient r is 1.

Correlations Correlations violent crime rate pct hs graduates violent crime rate[

Pearson Correlation

1

Sig. (2-tailed) N pct hs graduates

-.256 .070

51

51

Pearson Correlation

-.256

1

Sig. (2-tailed)

.070

N


51

51

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SPSS Assignment

(d) When the variable crate is correlate with variable educat the result of this regression is Model Summary

Model

R

R Square a

1

.256

Adjusted R

Std. Error of the

Square

Estimate

.066

.046

430.724

a. Predictors: (Constant), pct hs graduates a

Coefficients

Model 1 (Constant) pct hs graduates

Unstandardized

Standardized

95% Confidence Interval for

Coefficients

Coefficients

B

B

Std. Error

Beta

t

Sig. Lower Bound Upper Bound

2152.347

832.477

2.585 .013

479.421

3825.273

-20.197

10.893

-.256 -1.854 .070

-42.087

1.693

a. Dependent Variable: violent crime rate

(E) plot of the standardized residual against the predicted values in order to detect any outliers and to assess whether the relationship is linear and whether the residual variance is constant


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SPSS Assignment There is one residual greater than 4 and the trend indicates that there is approximately a linear relationship between crime rate and education. And from the scatter of points that tends to increase a little as the predicted value increases which indicating that the assumption of constant variance may not be appropriate. Question2.

The data file for question 2 is in the country.sav which contains the demographic information of 122 countries. (a). Explore the relationship between the variable using a scatter plot. Dependent variable= lifeexpf Independent variables= urban,docs,hospbed,gdp,and radio The result of the scatter plot matrix is shown below.

(b) The scatter plot matrix using the logarithm of the variables that don’t have a linear relationship is depicted below. Logarithm of the variables are= lndocs,lnbeds,lngdp, and lnradio As we can see easily from the scatter matrix plot the relationship is a linear relationship.


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SPSS Assignment

(C) using the forward selection to find the subset of variables that best explain the dependent variable. Dependent variable= lifeexp Independent variables= lndocs,urban,lnbeds,lngdp,lnradio


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SPSS Assignment

a

Coefficients

Standardized Unstandardized Coefficients Model 1

B (Constant) Natural log of doctors per 10000

2

(Constant) Natural log of doctors per 10000 Natural log of GDP

3

(Constant) Natural log of doctors per 10000 Natural log of GDP Natural log of radios per 100 people

Std. Error 57.232

.688

6.290

.318

42.138

3.206

4.261

.513

2.493

.519

41.697

3.140

4.123

.505

1.871 1.684

Coefficients Beta

t

Sig.

83.233

.000

19.792

.000

13.143

.000

.596

8.307

.000

.345

4.802

.000

13.278

.000

.577

8.168

.000

.566

.259

3.306

.001

.679

.142

2.482

.015

.880

a. Dependent Variable: Female life expectancy 1992

Number of doctors, GDP and number of radio are all positively related to life expectancy in females after controlling for the other variables. (d) The cook’s distance against the variable sequence Dependent variable= lifeexp Independent variable = lndocs,lngdp,lnradio As we can see from the result of the plot of the matrix of the cook’s distance the most influential countries are Chad, Afghanistan, an d Guinea.


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SPSS Assignment

(e) The distribution of the standardized residuals is shown below With some possible outliers we can say that the distribution is normally distributed with the normal distribution.


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SPSS Assignment

Question 3.

(a) (b) (c) (d) (e) (f) (g)

Independent sample T test Independent sample T test Paired T test Paired T test Independent T test Paired test Independent T test

Question 4. In the SPSS statistics box gives us the mean and standard deviation for each of the groups in this case age. It also gives the number of people in each group (N). Always check these values first.


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SPSS Assignment The first section of the Independent Samples Test output box gives us the results of Levene’s test for equality of variances. This tests whether the variance (variation) of ages for the two groups (populations) is the same. The outcome of this test determines which of the t-values that SPSS provides the correct one is. Since the significance value from the output [.82] is larger than .05 it should be the first column of the out table to be used, which is Equal variance is assumed. In the given the output from the question, the significance level for Levene’s test is .82. This is larger than the cut-off of .05. This means that the assumption of equal variances has not been violated; therefore, when it is reported the t-value used is the one in the first column from the output. From the out table the value of sig(2-tailed) in the first column is .000 less than .05 the required cut off there is a significance difference in the population’s mean ages of the two groups.

The value of t from the output table from the equal variance assumed column 3.9 and the values for N1 and N2 is the same from the output table 100. Up on substituting the value of the Eta squared is .0713. Then according to the guideline( proposed by Cohen,1998) for interoperating this value are .01=small effect .06= moderate effect .14= large effect For this particular question the, which have the effect size of .0713, effect is in the range of moderate and large. An independent sample test was conducted to compare the average ages of people who buy and who don’t buy a product. There is a significance difference in buying the product [mean 29.45,SD 15.56 and mean 38, SD 15.49];t(198)=-3.9,p<.001) The magnitude of the difference in the means was large (eta squared=.0713). Question 14. The data file for this question is school.sav and the aim is to check whether there are differences or not between the two groups that is above and below the median percentage of low income for all Chicago schools.

The group statics of the percent low income is shown below


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SPSS Assignment Group Statistics above or below median loinc Percent low income

N

above the median for low inc % 1993 below the median for low inc % 1993

Mean

Std. Deviation

Std. Error Mean

32

73.219

8.7498

1.5468

32

39.706

13.5002

2.3865

Independent Samples Test Levene's Test for Equality of Variances

t-test for Equality of Means 95% Confidence Interval of the

F Percent

Equal

low

variances

income

assumed

5.793

Sig.

t

.019 11.784

df

Sig. (2-

Mean

Std. Error

tailed)

Difference

Difference

Difference Lower

Upper

62

.000

33.5125

2.8439

27.8276

39.1974

11.784 53.138

.000

33.5125

2.8439

27.8087

39.2163

Equal variances not assumed

From the Levene’s test for equality of variances we have sig. value of .019 which is less than below the cut off value .05. The means that the variance between the two group (below and above) are not the same. Therefore the value of t-test is used the one that is in the raw of variance not assumed. To find out whether there is a significance difference between the two groups, refer to the column labeled sig(2-tailed), which appears under the section labeled t-test for unequal means. In combination with the Leven’s test result this value is 000 which is below .05. Therefore there is a significant difference in the means of the two groups.


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SPSS Assignment Group Statistics above or below median loinc average ACT score 1994

N

above the median for low inc % 1993 below the median for low inc % 1993

Mean

Std. Deviation

Std. Error Mean

32

15.022

.8746

.1546

32

16.700

2.1506

.3802



F average

Equal

ACT score

variances

1994

assumed Equal variances not assumed

16.501

Sig.

.000

t

df -

4.089

Mean

Std. Error

tailed)

Difference

Difference

Difference Lower

Upper

62

.000

-1.6781

.4104

-2.4985

-.8577

40.982

.000

-1.6781

.4104

-2.5070

-.8493

4.089

-

Sig. (2-

In the similar approach there is a significance difference between the means of the two groups. Because the significance value under the labeled sig(2-tailed) is 000 which is below .05


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SPSS Assignment

Question 16. The data file for this question is buying.sav and the aim is to test the null hypothesis of the following

1. Family buying score is the same when pictures are shown and when they are not. The result is shown below with its interpretation

Group Statistics Picture Accompanied Question Family Buying Score

N

Mean

Std. Deviation

Std. Error Mean

Pictures

48

159.08

27.564

3.979

No Pictures

50

168.00

21.787

3.081



F

Family

Equal variances

Buying

assumed

Score


1.382

Sig.

t

.243 -1.780

-1.772

df 96 89.42 9

Sig. (2-

Mean

Std. Error

tailed)

Difference

Difference

Difference Lower

Upper

.078

-8.917

5.008

-18.858

1.025

.080

-8.917

5.032

-18.915

1.081

From independent sample test we have the value of the significance .243 from the assumption of equal variance that is the Levene’s test and it is greater than the cut off that is .243>.05. This tells us which t-test to be used weather the Equal variance or the unequal variance assumption. But for this case since the Levene’s test value is greater than .05 then the t-test value is from the Equal variance assumption i.e value of t- that in the raw of equal variance. Therefore once the ttest value is determined the significance value can be identified. For this particular question the significance value that is P is .078. Since the value of p is greater than .05 [.078>.05] the null Msc program in Energy Technology, Mechanical Engineering

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SPSS Assignment hypothesis is not rejected. Therefore it is concluded that the family buying score is the same when the pictures are shown and when they are not. An independent sample t-test is conducted to compare the family buying score with picture and without picture. There are no significance difference in scores with picture (M=159,SD=27.564) and without picture (M=159,SD=21.787;t(96)=-1.78,p=.078]. The magnitude of the difference in the mean is moderate (eta square=.03). 2. Ho: The average buying score for the husband is the same with and without pictures. Ho is the null hypothesis. Group Statistics

Picture Accompani ed Question N Sum of husband's Pictures 48 buying scores No Pictures 50

Mean

Std. Deviation

Std. Mean

80.12

14.258

2.058

83.98

14.329

2.026

Error

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means

F Sum of husband's buying scores

Sig.

t

df

Equal variances .036 .849 -1.335 96 assumed Equal variances not assumed

95% Confidence Interval of the Sig. (2Mean Std. Error Difference tailed) Difference Difference Lower Upper .185

-3.855

2.889

-9.589

1.879

-1.335 95.874 .185

-3.855

2.888

-9.588

1.878


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SPSS Assignment With similar approach of the above, the significance for this part is .185 from [ sig 2-tailed] column and it is greater than the cut off (.05), the null hypothesis is not rejected. Still the average buying score for husband is the same with and without picture. An independent sample t-test is conducted to compare the family buying score with picture and without picture. There are no significance difference in scores with picture (M=80.12,SD=14.258) and without picture (M=83.98,SD=14.329;t(96)=-1.335,p=.185]. The magnitude of the difference in the mean is moderate (eta square=.018). 3.Ho : The average buying score for the wives is the same with and without pictures. Ho is the null hypothesis. Group Statistics Picture Accompanied Question

N

Sum of wife's buying scores Pictures No Pictures

Mean

Std. Deviation

Std. Error Mean

49

78.98

16.033

2.290

50

84.02

15.444

2.184

Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means 95% Confidence Interval of the Sig. (2-

F Sum of

Equal

wife's

variances

buying

assumed

scores

.025

Sig.

.876

t

-1.593 97


df tailed)

-1.593

96. 677

Mean

Std. Error

Difference

Difference

Difference Lower

Upper

.114

-5.040

3.164

-11.319

1.239

.115

-5.040

3.165

-11.322

1.241

With similar approach of the above, the significance for this part is .114 from [ sig 2-tailed] column and it is greater than the cut off (.05), the null hypothesis is not rejected. Still the average buying score for wives is the same with and without picture.


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SPSS Assignment An independent sample t-test is conducted to compare the family buying score with picture and without picture. There are no significance difference in scores with picture (M=78.98, SD=16.033) and without picture (M=84.02, SD=15.444;t(97)=-1.593,p=.114]. The magnitude of the difference in the mean is moderate (eta square=.025). Question 18.

A manufacturer of high-performance automobiles produces disc brakes that must measure 322 millimeters in diameter. Quality control randomly draws 16 discs made by each of eight production machines and measures their diameters. The appropriate test to determine whether or not the mean diameters of the brakes in each sample significantly differ from 322 millimeters is One Sample T Test to determine. The file for this question is brake.sav and its confidence interval is 90% The descriptive statics which displays the sample size, mean, standard deviation, and standard error for each of the eight samples The sample means disperse around the 322mm standard by what appears to be a small amount of variation.

One-Sample Statistics Machine Number 1

2

3

4

5

6

7

8

Disc Brake Diameter (mm)








N

Mean 16

16

16

16

16

16

16

16

Std. Deviation

3.219985E 2 3.220143E 2 3.219983E 2 3.219954E 2 3.220042E 2 3.220025E 2 3.220062E 2 3.219967E 2


Std. Error Mean

.0111568

.0027892

.0106913

.0026728

.0104812

.0026203

.0069883

.0017471

.0092022

.0023005

.0086440

.0021610

.0093303

.0023326

.0077085

.0019271

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SPSS Assignment

Since their confidence intervals lie entirely above 0.0, it is possible to say that machines 2, 5 and 7 are producing discs that are significantly wider than 322mm on the average. And similarly, because its confidence interval lies entirely below 0.0, machine 4 is producing discs that are not wide enough. Question19.

A physician is evaluating a new diet for her patients with a family history of heart disease. To test the effectiveness of this diet, 16 patients are placed on the diet for 6 months. Their weights and triglyceride levels are measured before and after the study, and the physician wants to know if either set of measurements has changed. The data are found in dietstudy.sav of SPSS sample files. Use appropriate test to determine whether there is a statistically significant difference between the pre- and post-diet weights and triglyceride levels of these patients Paired Samples Statistics Mean Pair 1

Pair 2

N

Std. Deviation

Std. Error Mean

Weight

198.38

16

33.472

8.368

Final weight

190.31

16

33.508

8.377

Triglyceride

138.44

16

29.040

7.260

Final triglyceride

124.38

16

29.412

7.353

Paired Samples Correlations N Pair 1

Weight & Final weight

Pair 2

Triglyceride & Final

Correlation

triglyceride

Sig.

16

.996

.000

16

-.286

.283

As the study was made to know if there is a statistically significant difference between the preand post-diet weights and triglyceride levels of these patients, a paired-samples t-test was appropriate test 1.

There is a statistically significant decrease in weight from pre-diet ( M = 198.38) to postdiet ( M = 190.31), t(15)=11.175. Since the probability value p (0.000) <. 0005 (twotailed) which is substantially smaller than our specified alpha value of .05, there is a significant difference in weight of the patients between the pre- and post-diet measurements. The mean decrease in weight is 8.062 with a 95% confidence interval ranging from 6.525 to 9.600. The t value is used to calculate the effect size statistic squared (eta squared statistic). Eta squared =





  ( )


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SPSS Assignment 

Eta squared =

.

. ( )

= 0.893

According to Cohen 1988, pp. 284–7 guidlines, the Eta squared value .01=small effect, .06=moderate effect, .14=large effect. Since the Eta squared value obtained 0.893 is greater than 0.14, there is a large effect with a significant difference in weight of the patients between the pre- and post-diet measurements. 2.

There is a statistically significant decrease in triglyceride from pre-diet ( M = 138.44) to post-diet ( M = 124.38), t(15)=1.200. Since the probability value p (0.249) <. 0005 (twotailed) which is substantially smaller than our specified alpha value of .05, there is a significant difference in triglyceride of the patients between the pre- and post-diet measurements. The mean decrease in triglyceride is 14.062 with a 95% confidence interval ranging from -10.915 to 39.040. The effect size statistic squared (eta squared statistic): 

Eta squared =

.

. ( )

= 0.0876

Since the Eta squared value obtained 0.0876 is in between 0.06 and 0.14, there is moderate effect with a significant difference in triglyceride of the patients between the pre- and post-diet measurements.


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Assignment SPSS Word2

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