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. Deviation
Std. Error
Mean
Pair 1
Academic
Performance_Average
Marks in 2012
51.28 106 20.533 1.994
Academic Performance _
Average Marks in 2013
57.15 106 18.777 1.824
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
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 Mean
Std.
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.
2
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quantitative data analysis using spss

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