1. Data Analysis Using SPSS EDU5950 SEM1 2014-15 Test of Differences Between Means
Assoc. Prof. Dr. Rohani Ahmad Tarmizi
Institute for Mathematical Research/
Faculty of Educational Studies
UPM

2. Overview
First objective – learn what is important in choosing analyses, and information about some of the more common statistical analyses
Second objective – will get a data set and walk through how to conduct some analyses of differences between means

3. Statistical Tools For Inferential Statistics
PARAMETRIC TESTS:
Test of hypothesis of differences between means - Z-test, t-test, F-test, MANOVA
Test of hypothesis of relationship – Pearson r, Point-biserial, Regression
NON-PARAMETRIC TESTS:
Chi-square,
Mann-Whitney,
Kruskal Wallis,
Spearman rho,
Cramer’s V, Lambda, dll.

4. In most research projects, it is likely that you will use quite a variety of different types of statistics, depending on the question you are addressing and the nature (level of measurement) of the data that you have.
It is therefore important that you have a basic understanding of the different statistical tools, the type of objectives/research questions/hypotheses to address and the underlying assumptions and requirements.

5. Summary of Statistical Tools For Descriptive Analyses
Frequency/percentage table,
Pie or bar Charts,
Histogram
Frequency Polygon,
Cross-tabulation
Scatter diagram
Mean, Median, Mode, Maximum, Minimum
Range, Variance, Standard Deviation, Coefficient of variation, Standard Scores

6. ACTIVITY 1- COMPARISON OF MEANS
OF TWO GROUPS

7. t-test EXPLORING DIFFERENCES BETWEEN TWO GROUPS
t-tests are used when you have two groups (e.g. males and females) or two sets of data (before and after), and you wish to compare the mean score on some continuous variable.
There are two main types of t-tests.
Paired sample t-tests (also called repeated measures) are used when you are interested in changes in scores for subject tested at Time 1, and then at Time 2 (often after some intervention or event). The samples are ‘related’ because they are the same people tested each time.
Independent sample t-tests are used when you have two different (independent) groups of people (males and females), and you are interested in comparing their scores. In this case, you collect information on only one occasion, but from two different sets of people.

8. CLICK ANALYZE =>COMPARE MEANS You will get the following Sub-menus
TO MAKE COMPARISONS BETWEEN GROUPS ON ANY MEASURED VARIABLES AT INTERVAL AND RATIO LEVEL
CLICK ANALYZE =>COMPARE MEANS
You will get the following Sub-menus
MEANS
ONE-SAMPLE T-TEST
INDEPENDENT SAMPLES T-TEST
PAIRED SAMPLES T-TEST
ONE-WAY ANOVA

9. EXAMPLE OF RESEARCH QUESTION
PURPOSE
EXAMPLE OF RESEARCH QUESTION
PARAMETRIC STATISTIC
INDEPENDENT VARIABLE
DEPENDENT VARIABLE
Comparing means of two groups
Is there a difference in instructors’ efficacy in teaching and learning mathematics as perceived by students of different gender?
Independent t-test
One categorical independent variable gender of two levels-males and females
One continuous dependent variable
students’ perception on instructors’ efficacy in teaching and learning

10. To Compare Means of Two Groups
Click: Analyze>Compare means>Independent T-test
You will get a Independent T-test dialog box
Select your variables – Test variables & Group variables
Click OK

11. DECISION MATRIX
HYPOTHESIS
ALPHA VALUE
SIGNIFICANT VALUE
(FROM THE SPSS OUTPUT)
EVALUATING
DECISION
CONCLUSION
There is no significant difference in variance of students’ perception on instructors’ efficacy in T&L
of by different gender
0.05
.351
SIG.V > α
Fail to reject null hypothesis,
Accept null hypothesis
There is no significant difference in variance of beliefs on teacher’s role scores for students of different gender.
Choose t from the equal variances assumed row
There is a significant difference in variance of students’ perception on instructors’ efficacy in T&L by different gender

12. DECISION MATRIX
HYPOTHESIS
ALPHA VALUE
SIGNIFICANT VALUE
(FROM THE SPSS OUTPUT)
EVALUATING
DECISION
CONCLUSION
There is no significant difference in students’ perception on instructors’ efficacy in T&L by different gender
0.05
.926
SIG.V > α
Fail to reject null hypothesis,
Accept null hypothesis
There is no significant difference in students’ perception on instructors’ efficacy in T&L by gender, t (60) = -.094, p> ( or p=.926)
There is a significant difference in students’ perception on instructors’ efficacy in T&L by different gender

13. Independent Samples Test
Group Statistics
Gender N
Mean
Std. Deviation
Std. Error Mean
INSTRUCTORS’ EFFICACY
lelaki 21
3.9490
.89190
.19463
perempuan 41
3.9721
.93662
.14628
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means F
Sig. t df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
INSTRUCTORS’ EFFICACY
Equal variances assumed
.883
.351
-.094 60
.926
.24740
.47173
Equal variances not assumed
-.095
42.237
.925
.24347
.46811

14. EXAMPLE OF RESEARCH QUESTION
PURPOSE
EXAMPLE OF RESEARCH QUESTION
PARAMETRIC STATISTIC
INDEPENDENT VARIABLE
DEPENDENT VARIABLE
Comparing means of two groups
Is there a difference in students’ perception of mathematics instructors’ role in making the students enjoy learning maths with making maths’ lessons interesting
Dependent t-test -
Two continuous dependent variable:
students’ perception of mathematics inastructors’ role in making the students enjoy learning maths with making maths’ lessons interesting
Item1 vs Item 3

15. Paired Samples Correlations
To Compare Means of Two Dependent Groups
Click: Analyze>Compare means>Paired Sample T-test
You will get a Paired Sample T-test dialog box
Select your variables – Paired variables
Click OK
Paired Samples Correlations N
Correlation
Sig.
Pair 1
My instructor wants us to enjoy learning maths & My teacher try to make mathematics lessons interesting 63
.708
.000
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
My instructors wants us to enjoy learning maths - My teacher try to make mathematics lessons interesting
-.238
1.174
.148
-.534
.058
-1.610 62
.112

16. DECISION MATRIX
HYPOTHESIS
ALPHA VALUE
SIGNIFICANT VALUE
(FROM THE SPSS OUTPUT)
EVALUATING
DECISION
CONCLUSION
There is no significant difference in students’ perception of mathematics instructors’ role in making the students enjoy learning maths with making maths’ lessons interesting
0.05
.112
SIG.V > α
Fail to reject null hypothesis,
Accept null hypothesis
There is no significant difference in students’ perception of mathematics instructors’ role in making the students enjoy learning maths with making maths’ lessons interesting, t (62) = , p> ( or p=.112)
There is a significant difference in students’ perception of mathematics instructors’ role in making the students enjoy learning maths with making maths’ lessons interesting

17. ACTIVITY 2
ANOVA

18. EXPLORING DIFFERENCES BETWEEN GROUPS
One-way analysis variance
One-way analysis variance is similar to a t-test, but is used when you have two or more groups and you wish to compare their mean scores on a continuous variable.
It is called one-way because you are looking at the impact of only one independent variable on your dependent variable.
A one-way analysis of variance (ANOVA) will let you know whether your groups differ, but it won’t tell you where the significant difference is (gp1/gp2, gp3/gp4 etc).
You can conduct post-hoc comparisons to find out which groups are significantly different from one another.
You could also choose to test differences between specific groups, rather than comparing all the groups by using planned comparisons. Similar to t-tests, there are two types of one-way ANOVAs: repeated measures ANOVA (same people on more than two occasions), and between-groups (or independent samples) ANOVA, where you are comparing the mean scores of two or more different groups of people.

19. EXAMPLE OF RESEARCH QUESTION
PURPOSE
EXAMPLE OF RESEARCH QUESTION
PARAMETRIC STATISTIC
INDEPENDENT VARIABLE
DEPENDENT VARIABLE
Comparing means of three groups
Is there a difference in students’ perception of instructors’ efficacy in T&L mathematics by
race?
One-way between groups ANOVA
One categorical independent variable (three levels of race)
One continuous dependent variable
students’ perception of instructors’ efficacy in T&L mathematics

20. 95% Confidence Interval for Mean
To Compare Means of Three or More Groups
Click: Analyze>Compare means>One-Way ANOVA
You will get a One-Way ANOVA dialog box
Select your variables – Dependent variables & Factor or Group variables
Click: Options
Click OK
Descriptives
INSTRUCTORS’_EFFICACY N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
MELAYU 14
4.2704
.73282
.19586
3.8473
4.6935
3.07
5.36
CINA 40
3.7339
.96118
.15198
3.4265
4.0413
2.21
5.71
INDIA 8
4.5804
.46673
.16501
4.1902
4.9706
3.86
5.07
Total 62
3.9643
.91443
.11613
3.7321
4.1965
ANOVA
INSTRUCTORS’ EFFICACY
Sum of Squares df
Mean Square F
Sig.
Between Groups
6.471 2
3.235
4.286
.018
Within Groups
44.537 59
.755
Total
51.008 61

21. DECISION MATRIX
HYPOTHESIS
ALPHA VALUE
SIGNIFICANT VALUE
(FROM THE SPSS OUTPUT)
EVALUATING
DECISION
CONCLUSION
There is no significant difference in students’ perception of instructors’ efficacy in T&L mathematics by race?
0.05
.018
SIG.V < α
Reject null hypothesis,
Accept alternative hypothesis
There is significant difference in students’ perception of instructors’ efficacy in T&L mathematics by race, F(2,59) = 4.29, p<.05.
There is a significant difference in students’ perception of instructors’ efficacy in T&L mathematics by race?

22. Two-way analysis of variance
Two-way analysis of variance allows you to test the impact of two independent variables on one dependent variable.
The advantage of using the two-way ANOVA is that it allows you to test for an interaction effect – that is, when the effect of one independent variable is influenced by another; for example, when you suspect that optimism increases with age, but only for males.
It also tests for ‘main effects’ – that is, the overall effect of each independent variable (e.g. sex, age).
There are two different two-way ANOVAs: between - groups ANOVA (when the groups are different) and repeated measures ANOVA (when the same peoples are tested on more than one occasion).
Some research designs combine both between-group and repeated measures in the one study. These are referred to as ‘Mixed Between-Within Designs’, or ‘Split Plot’.

23. NON-PARAMETRIC ALTERNATIVE
PURPOSE
EXAMPLE OF QUESTION
PARAMETRIC STATISTIC
NON-PARAMETRIC ALTERNATIVE
INDEPENDENT VARIABLE
DEPENDENT VARIABLE
ESSENTIAL FEATURES
Comparing groups (cont.)
Is there a significant difference in job stress between instructors’ of different leadership style? Different gender? Is there a significant Interaction effect on job stress based on gender and leadership style?
Analysis if covariance (ANCOVA)
None
One or more categorical independent variables (two or more levels) – leadership style, gender
One continuous dependent variable -job stress

24. Click Analyze => General Linear Model => Univariate…
2. At the Univariate dialog box, enter Y into Dependent variable box, and X1 and X2 into Fixed Factors box.

25. 3. Click the option button and select the followings

27. Between-Subjects Factors Descriptive Statistics
Value Label N
gender 1
male 30 2
female
leadership style
autocratic 20
democratic 3
laisserfaire
Descriptive Statistics
Dependent Variable:job stress level
gender
leadership style
Mean
Std. Deviation N
male
autocratic 10
democratic
laisserfaire
Total 30
female 20 60

28. Levene's Test of Equality of Error Variancesa
Dependent Variable:job stress level F
df1
df2
Sig.
.874 5 54
.505
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Design: Intercept + gender + leadershipstyle + gender * leadershipstyle
Tests of Between-Subjects Effects
Dependent Variable:job stress level
Source
Type III Sum of Squares df
Mean Square F
Sig.
Partial Eta Squared
Corrected Model a 5
7.256
.000
.402
Intercept 1
.991
gender
12.221
.001
.185
leadershipstyle 2
10.612
.282
gender * leadershipstyle
78.050
1.417
.251
.050
Error 54
55.098
Total 60
Corrected Total 59
a. R Squared = .402 (Adjusted R Squared = .346)

29. 3. gender * leadership style
Dependent Variable:job stress level
gender
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
male
71.933
1.355
69.216
74.650
female
78.633
75.916
81.350
2. leadership style
Dependent Variable:job stress level
leadership style
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
autocratic
81.150
1.660
77.822
84.478
democratic
70.500
67.172
73.828
laisserfaire
74.200
70.872
77.528
3. gender * leadership style
Dependent Variable:job stress level
gender
leadership style
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
male
autocratic
75.800
2.347
71.094
80.506
democratic
69.100
64.394
73.806
laisserfaire
70.900
66.194
75.606
female
86.500
81.794
91.206
71.900
67.194
76.606
77.500
72.794
82.206

31. Presenting the results of Factorial ANOVA
A factorial ANOVA was conducted to explore the impact of gender and leadership style of principals on their teachers’ job stress level. Three leadership style was explored viz-a-viz autocratic, democratic and laisserfaire style. There was a statistically significant main effect for both gender and leadership style on teachers’ job stress level. Therefore gender of principals has an impact on teachers’ job stress level significantly, F (1,60) = 12.22, p = In addition, there is also significant impact of principals’ leadership style on job stress of teachers significantly, F (2,60) = 10.61, p = However the interaction effect between gender and leadership style was not statistically significant F ((2, 60) = 1.42, p = .25.

32. Post-hoc comparison using Tukey HSD test
indicated that the mean job stress score for
the female (M=78.63, SD=8.98) is significantly
higher than the male teachers (M=71.93,
SD=8.22).
The mean job stress scores between the three
groups of leadership style indicated that the
autocratic style impacted significantly higher
stress level compared to democratic and
laisserfaire. However there is no significant
difference in stress level between the democratic
and lasserfaire leadership style.

33. NON-PARAMETRIC ALTERNATIVE
REPEATED MEASURES ANOVA
PURPOSE
EXAMPLE OF QUESTION
PARAMETRIC STATISTIC
NON-PARAMETRIC ALTERNATIVE
INDEPENDENT VARIABLE
DEPENDENT VARIABLE
Comparing groups (cont.)
Is there a significant difference in fear of statistics at three different time?
Repeated measure analysis
None
One or more categorical independent variables - time1, time2, time3
One continuous dependent variable
fear of statistics at three different time?
FOLLOW THE PROCEDURES ON THE NEXT SLIDE

35. NON-PARAMETRIC ALTERNATIVE
PURPOSE
EXAMPLE OF QUESTION
PARAMETRIC STATISTIC
NON-PARAMETRIC ALTERNATIVE
INDEPENDENT VARIABLE
DEPENDENT VARIABLE
ESSENTIAL FEATURES
Comparing groups (cont.)
Is there a significant difference in fear of statistics at three different time?
Repeated measure analysis
None
One or more categorical independent variables - time1, time2, time3
One continuous dependent variable
fear of statistics at three different time?

36. Descriptive Statistics
Mean
Std. Deviation N
fear of stats time1
40.17
5.160 30
fear of stats time2
37.50
5.151
fear of stats time3
35.23
6.015
Multivariate Testsc
Effect
Value F
Hypothesis df
Error df
Sig.
Partial Eta Squared
Noncent. Parameter
Observed Powerb
fear_statistics
Pillai's Trace
.635
24.356a
2.000
28.000
.000
48.712
1.000
Wilks' Lambda
.365
Hotelling's Trace
1.740
Roy's Largest Root
a. Exact statistic
b. Computed using alpha = .05
c. Design: Intercept
Within Subjects Design: fear_statistics

37. Mauchly's Test of Sphericityb Tests of Within-Subjects Effects
Measure:MEASURE_1
Within Subjects Effect
Mauchly's W
Approx. Chi-Square df
Sig.
Epsilona
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
dimension1
fear_statistics
.342
30.071 2
.000
.603
.615
.500
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.
a. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.
b. Design: Intercept
Within Subjects Design: fear_statistics
Tests of Within-Subjects Effects
Measure:MEASURE_1
Source
Type III Sum of Squares df
Mean Square F
Sig.
Partial Eta Squared
Noncent. Parameter
Observed Powera
fear_statistics
Sphericity Assumed 2
41.424
.000
.588
82.849
1.000
Greenhouse-Geisser
1.206
49.958
Huynh-Feldt
1.230
50.943
Lower-bound
Error(fear_statistics) 58
4.416
34.974
7.323
35.664
7.182
29.000
8.832
a. Computed using alpha = .05

38. A repeated measures ANOVA was carried out
A repeated measures ANOVA was carried out. Assumptions of normality, homogeneity of variance and sphericity were met. Results showed that differences between conditions were significant, F (2,35) = , p=.001. An overall effect size of .588 (partial eta-squared) showed that 60% of the variation in fear of statistics scores can be accounted by differing time.