quantitative data analysis using spss

QUANTITATIVE DATA ANALYSIS

USING SPSS

Lecture by Viraiyan Teeroovengadum

Department of Management, Faculty of Law and Management, University of Mauritius

Hypothesis Testing

(Testing for Differences)

3.0

3.1 One-Sample T Test (Parametric)

3.2 Independent-Samples T Test (Parametric)

3.3 Paired-Samples T Test (Parametric)

3.4 One-Way ANOVA (Parametric)

3.5 One-Sample Median Test (Non-Parametric)

3.6 Mann-Whitney U Test (Non-Parametric)

3.7 Wilcoxon Sign Rank Test (Non-Parametric)

3.8 Kruskal-Wallis Test (Non-Parametric)

3.9 Chi-Square Test (Non-Parametric)



Introduction

3.1 One-Sample T Test

Testing for differences between test value (hypothesised population value) and obtained value



When to Use the Test?3.2



The One-Sample T-Test can be used when:

• We want to compare a sample result to a population test value

• The variable is measured at scale level

• Variable follows a normal distribution

3.2 Independent-Samples T Test

Testing for differences between two independent samples / groups






The Independent-Samples T Test can be used when:

• The independent variable consists of two categories (considered as two

samples)

• The two samples/ groups are independent (the two means are from different

cases)

• The dependent variable is measured at scale level

• The dependent variable follows a normal distribution for the two groups

• The variances are homogeneous

Performing the test using SPSS3.2



Preliminary Steps

Analyse Compare Means Independent-Samples T Test




Further Steps:

1. Transfer the dependent variable to the test variable list.

2. Transfer the grouping (categorical) variable

3. Define the grouping variable

Interpreting the results3.2



As a general guideline the following should be reported when interpreting the results of an

independent-samples t test:

1. The descriptive statistics (Mean and Standard Deviation) for both samples. Including a couple

of statements.

2. Explain that an independent-samples t test shall be used to test for statistically significant

differences between the two means

3. Hypotheses can be re stated

4. Report the results for assumptions of normality and equality of variances

5. Interpret the results of the t test, comparing the obtained p-value (significance value) to the

significance level set.

6. Statement to describe the meaning of the result

7. Report the effect size

Interpreting the results (Example)3.2



Research Question:

Is there a difference between the perception of undergraduate and postgraduate students

with respect to the quality of infrastructure at the University of Mauritius?

Hypothesis:

H0: There is no significant difference between the perception of undergraduate and

postgraduate students with respect to the quality of infrastructure at the University of

Mauritius (µundergraduate = µpostgraduate)

H1: There is a significant difference between the perception of undergraduate and

postgraduate students with respect to the quality of infrastructure at the University of

Mauritius (µundergraduate ≠ µpostgraduate)







Interpretation of the results:

The undergraduate students group (N=97) had a score of M=2.99 with regards to their perception

of infrastructure quality at UoM. By comparison, the mean score for postgraduate students was

lower (M=2.86). To test the hypothesis that undergraduate students and postgraduate students had

statistically significantly different mean perception of infrastructure quality, an independent-

samples t test was performed.

The undergraduate and postgraduate distributions were sufficiently normal for the purposes of

conducting a t test. Moreover, the assumption of homogeneity of variances was tested and

satisfied via Levene’s F Test, F(205) = 0.04, p= 0.947.

The independent-samples t test was associated with a statistically significant effect, t(205) = -2.08,

p = 0.038. Thus, the mean score for postgraduate students was statistically significantly lower than

the mean score for undergraduate students. In other words, the quality of infrastructure at UoM is

perceived to be lower by postgraduate students as compared to undergraduate students.

3.3 Paired-Samples T Test

Testing for differences between two dependent samples / groups






The Paired-Samples T Test can be used when:

• The independent variable consists of two categories (considered as two

samples)

• The two samples/groups are related/dependent (the two means are from the

same cases but correspond to scores measured at different points in time)


• The difference score follows a normal distribution




Preliminary Steps

Analyse Compare Means Paired-Samples T Test




Further Steps:

1. Transfer the first variable (time period 1) to variable 1

2. Transfer the second variable (time period 2) to variable 2




As a general guideline the following should be reported when interpreting the results of a paired-

samples t test:

1. The descriptive statistics (Mean and Standard Deviation) for both samples (time periods).

2. Explain that a paired-samples t test shall be used to test for statistically significant differences

between the two means


4. Report the results for assumptions of normality of score differences

5. Interpret the results of the t test, comparing the obtained p-value (significance value) to the







Research Question:

Has there been an improvement in the academic performance of students in 2012 as

compared to 2013?

Hypothesis:

H0: There is no significant improvement in the academic performance of students in 2012

as compared to their academic performance in 2013 (µ2013 = µ2012)

H1: There is a significant improvement in the academic performance of students in 2012 as

compared to their academic performance in 2013 (µ2013 > µ2012)




Paired Samples Statistics

Mean N Std. DeviationStd. Error

Mean

Pair 1

Academic

Performance_Average

Marks in 2012

51.28 106 20.533 1.994

Academic Performance _

Average Marks in 201357.15 106 18.777 1.824

Paired Samples Test

Paired Differences

t dfSig. (2-

tailed)MeanStd.

Deviation

Std. Error

Mean

95% Confidence

Interval of the

Difference

Lower Upper

Pair 1

Academic

Performance_Aver

age Marks in 2012

- Academic

Performance _

Average Marks in

2013

-5.868 12.521 1.216 -8.279 -3.456 -4.825 105 .000





To test the hypothesis that the academic performance of students in 2012 (M= 51.28, SD = 20.53)

had improved significantly in 2013 (M= 57.15, SD = 18.78), a paired-samples t test was performed.

Prior to conducting the analysis, the assumption of normally distributed difference scores was

examined. The assumption was considered satisfied, as the skewness and kurtosis were estimated

at 0.10 and -1.12, respectively, which is less than the maximum allowable values for a t-test (i.e,

skewness │2.0 │ and kurtosis │9.0 │; Posten, 1984).

The null hypothesis of equal academic performance means was rejected, t = - 4.83, p < 0.05. Thus

the mean of academic performance of students in 2013 was statistically significantly higher than the

mean of academic performance in 2012. In other words, students performed better in 2013 than in

2012.

3.4 One-Way ANOVA

Testing for differences between more than 2 independent samples / groups






The One-Way ANOVA can be used when:

• The independent variable consists of more than two categories (considered as

more than two samples)

• The k samples/ groups are independent (the k means are from different cases)


• The dependent variable follows a normal distribution for each sample

• Variances are homogeoneous




Preliminary Steps

Analyse Compare Means One-Way ANOVA




Further Steps:

1. Transfer the dependent variable to the dependent list.

2. Transfer the grouping (categorical) variable to factor list

3. Click on Post Hoc and select Tukey




As a general guideline the following should be reported when interpreting the results of a One-Way

ANOVA:

1. The descriptive statistics (Mean and Standard Deviation) for each samples. Including a couple

of statements.

2. Explain that a one-way ANOVA test shall be used to test for statistically significant differences

between the multiple means


4. Report the results for assumptions of normality and equality of variances

5. Interpret the results of the F test, comparing the obtained p-value (significance value) to the







Research Question:

Is there a difference between the four ISO certified schools with regards to perceived ISO

Benefits?

Hypothesis:

H0: There is no significant difference between the four ISO certified schools with regards to

perceived ISO Benefits

H1: There is a significant difference between the four different ISO certified schools with

regards to perceived ISO Benefits




ANOVA

Benef

Sum of Squares df Mean Square F Sig.

Between Groups 28.081 3 9.360 27.782 .000

Within Groups 37.398 111 .337

Total 65.479 114

Descriptives

Benef

N MeanStd.

Deviation

Std.

Error

95% Confidence Interval for

Mean Minimu

m

Maxim

umLower

Bound

Upper

Bound

Hindu Girls College 38 3.6661 .54801 .08890 3.4860 3.8462 2.38 5.00

Prof Basdeo

Bissoondoyal

Secondary School

47 4.3191 .46227 .06743 4.1834 4.4549 3.50 5.00

Mauritius College 17 3.2537 .86390 .20953 2.8095 3.6979 1.50 4.75

SSS Sodnac 13 2.9375 .61343 .17014 2.5668 3.3082 2.00 4.00

Total 115 3.7897 .75788 .07067 3.6497 3.9297 1.50 5.00




Multiple Comparisons

Dependent Variable: Benef Tukey HSD

(I) Name of School/Department (J) Name of School/Department Mean Difference

(I-J)

Std. Error Sig. 95% Confidence Interval

Lower Bound Upper Bound

Hindu Girls College Prof Basdeo Bissoondoyal

Secondary School

-.65303* .12663 .000 -.9833 -.3227

Mauritius College .41244 .16937 .076 -.0293 .8542

SSS Sodnac .72862* .18650 .001 .2421 1.2151

Prof Basdeo Bissoondoyal

Secondary School

Hindu Girls College .65303* .12663 .000 .3227 .9833

Mauritius College 1.06547* .16428 .000 .6370 1.4940

SSS Sodnac 1.38165* .18189 .000 .9072 1.8561

Mauritius College Hindu Girls College -.41244 .16937 .076 -.8542 .0293


Secondary School

-1.06547* .16428 .000 -1.4940 -.6370

SSS Sodnac .31618 .21386 .454 -.2417 .8740

SSS Sodnac Hindu Girls College -.72862* .18650 .001 -1.2151 -.2421


Secondary School

-1.38165* .18189 .000 -1.8561 -.9072

Mauritius College -.31618 .21386 .454 -.8740 .2417

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





The descriptive statistics associated with perceived benefits of ISO certification across the four

schools are reported in table x. It can be seen that the SSS Sodnac school was associated with the

numerically smallest mean level of perceived ISO benefits (M=2.94) and the Prof Basdeo

Bissoondoyal Secondary School was associated with numerically the highest mean level of

perceived ISO benefits (M=4.32).

In order to test the hypothesis that school difference had an effect on perceived ISO benefits, a

one-way between-groups ANOVA was performed. Prior to conducting the ANOVA, the assumption

of normality was evaluated and determined to be satisfied as the three groups’ distributions were

associated with skewness and kurtosis less that │2.0 │ and │9.0 │, respectively (Schmider et al.,

2010). The assumption of homogeneity of variances was tested and was not satisfied, based on

Levene’s F Test, F(3, 111) = 3.43, p = 0.019 < 0.05. The Welch Test was therefore used to account

for that.





The independent between-groups ANOVA yielded a statistically significant effect, F(3, 35.07) =

27.79, p < 0.05, = 0.429. Thus the null hypothesis of no differences between the means was

rejected, and 42.9% of the variance in perceived ISO benefits was accounted for by the school

difference. To evaluate the nature of the differences between the four means further, the

statistically significant ANOVA was followed up with a multiple comparison test.

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Data & Analytics

quantitative data analysis using spss