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

Data Analysis Using SPSSEDU5950

SEM1 2014-15Test of Differences Between Means

Assoc. Prof. Dr. Rohani Ahmad TarmiziInstitute for Mathematical Research/

Faculty of Educational StudiesUPM

OverviewFirst 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

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.

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.

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

ACTIVITY 1- COMPARISON OF MEANS OF TWO GROUPS

EXPLORING DIFFERENCES BETWEEN TWO GROUPS

1.t-test 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.

• 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

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 variablestudents’ perception on instructors’ efficacy in teaching and learning

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

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&Lof 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

DECISION MATRIX


SIGNIFICANT VALUE



There is no significant difference in students’ perception on instructors’ efficacy in T&L by different gender



There is no significant difference in students’ perception on instructors’ efficacy in T&L by gender, t (60) = -.094, p> .05. ( or p=.926)

There is a significant difference in students’ perception on instructors’ efficacy in T&L by different gender

DECISION MATRIX

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 -.02315 .24740 -.51803 .47173

Equal variances not assumed

-.095 42.237 .925 -.02315 .24347 -.51440 .46811

Group Statistics

GenderN Mean Std. Deviation Std. Error Mean

INSTRUCTORS’

EFFICACY

lelaki 21 3.9490 .89190 .19463

perempuan 41 3.9721 .93662 .14628


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

Paired Samples Correlations

N

Correlati

on 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

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

HYPOTHESIS ALPHA VALUE SIGNIFICANT VALUE



There is no significant difference in students’ perception of mathematics instructors’ role in making the students enjoy learning maths with making maths’ lessons interesting



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) = -1.160, p> .05. ( 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

DECISION MATRIX

ACTIVITY 2 ANOVA

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.




DEPENDENT VARIABLE

Comparing means of three groups

Is there a difference in students’ perception of instructors’ efficacy in T&L mathematics byrace?

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

Descriptives

INSTRUCTORS’_EFFICACY

N MeanStd.

Deviation

Std.

Error

95% Confidence Interval

for Mean

Minimu

m

Maximu

m

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 2.21 5.71

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

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


SIGNIFICANT VALUE



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?

DECISION MATRIX

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’.

PURPOSE EXAMPLE OF QUESTION


NON-PARAMETRIC ALTERNATIV

E


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

1. 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.

3. Click the option button and select the followings

Between-Subjects Factors

Value Label N

gender 1 male 30

2 female 30

leadership

style

1 autocratic 20

2 democratic 20

3 laisserfaire 20

Descriptive Statistics

Dependent Variable:job stress level

genderleadership style Mean

Std. Deviation N

male autocratic 75.8000 6.64664 10

democratic69.1000 7.72370 10

laisserfaire70.9000 9.33869 10

Total 71.9333 8.22080 30

female autocratic 86.5000 6.99603 10

democratic71.9000 8.26573 10


Total 78.6333 8.98460 30

Total autocratic 81.1500 8.61623 20

democratic70.5000 7.91734 20


Total 75.2833 9.18195 60

Levene's Test of Equality of Error Variancesa


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


Source

Type III Sum of

Squares df Mean Square F Sig.

Partial Eta

Squared

Corrected Model 1998.883a 5 399.777 7.256 .000 .402

Intercept 340054.817 1 340054.817 6171.801 .000 .991

gender 673.350 1 673.350 12.221 .001 .185

leadershipstyle 1169.433 2 584.717 10.612 .000 .282

gender * leadershipstyle 156.100 2 78.050 1.417 .251 .050

Error 2975.300 54 55.098

Total 345029.000 60

Corrected Total 4974.183 59

a. R Squared = .402 (Adjusted R Squared = .346)

1. gender


gender Mean Std. Error


Lower Bound Upper Bound

male 71.933 1.355 69.216 74.650

female 78.633 1.355 75.916 81.350

2. leadership style


leadership style Mean Std. Error



autocratic 81.150 1.660 77.822 84.478

democratic 70.500 1.660 67.172 73.828

laisserfaire 74.200 1.660 70.872 77.528

3. gender * leadership style


gender

leadership

style Mean Std. Error



male autocratic 75.800 2.347 71.094 80.506

democratic 69.100 2.347 64.394 73.806

laisserfaire 70.900 2.347 66.194 75.606

female autocratic 86.500 2.347 81.794 91.206

democratic 71.900 2.347 67.194 76.606

laisserfaire 77.500 2.347 72.794 82.206

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 = .001. In addition, there is also significant impact of principals’ leadership style on job stress of teachers significantly, F (2,60) = 10.61, p = .000. However the interaction effect between gender and leadership style was not statistically significant F ((2, 60) = 1.42, p = .25.

Post-hoc comparison using Tukey HSD test indicated that the mean job stress score for the female (M=78.63, SD=8.98) is significantlyhigher than the male teachers (M=71.93, SD=8.22). The mean job stress scores between the threegroups of leadership style indicated that theautocratic style impacted significantly higherstress level compared to democratic andlaisserfaire. However there is no significantdifference in stress level between the democratic and lasserfaire leadership style.



NON-PARAMETRIC ALTERNATIVE


DEPENDENT VARIABLE


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 variablefear of statistics at three different time?

REPEATED MEASURES ANOVA

FOLLOW THE PROCEDURES ON THE NEXT SLIDE



NON-PARAMETRIC ALTERNATIV

E


DEPENDENT VARIABLE

ESSENTIAL FEATURES


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 variablefear of statistics at three different time?

Descriptive Statistics

Mean Std. Deviation N

fear of stats time1 40.17 5.160 30



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 .635 48.712 1.000

Wilks' Lambda .365 24.356a 2.000 28.000 .000 .635 48.712 1.000

Hotelling's

Trace

1.740 24.356a 2.000 28.000 .000 .635 48.712 1.000

Roy's Largest

Root

1.740 24.356a 2.000 28.000 .000 .635 48.712 1.000

a. Exact statistic

b. Computed using alpha = .05

c. Design: Intercept

Within Subjects Design: fear_statistics

Mauchly's Test of Sphericityb

Measure:MEASURE_1

Within Subjects Effect

Mauchly's

W

Approx. Chi-

Square df Sig.

Epsilona

Greenhouse-

Geisser Huynh-Feldt Lower-bound

dimension1

fear_statistic

s

.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

365.867 2 182.933 41.424 .000 .588 82.849 1.000

Greenhouse-

Geisser

365.867 1.206 303.368 41.424 .000 .588 49.958 1.000

Huynh-Feldt 365.867 1.230 297.506 41.424 .000 .588 50.943 1.000

Lower-bound 365.867 1.000 365.867 41.424 .000 .588 41.424 1.000

Error(fear_statisti

cs)

Sphericity

Assumed

256.133 58 4.416

Greenhouse-

Geisser

256.133 34.974 7.323

Huynh-Feldt 256.133 35.664 7.182

Lower-bound 256.133 29.000 8.832

a. Computed using alpha = .05

• 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) = 41.424, 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.

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

Documents

independent sample ttests

test of differences

paired sample ttests

main types of t

different statistical

different sets of

analyses of differences

sets of data