Quantitative data analysis for social science using PASW/SPSS (Part 2) Conducted by Dr Shamala

Workshop Outcomes At the end of this workshop, you will be able to: Select appropriate statistical analysis according to the research questions. Interpret outputs of statistical results according to APA standards. Prepared by Dr. Shamala 2

Data Analysis derives from Research Questions Research Questions Describing Frequency/% Measures of Central Tendency Relationship Pearson Correlation Partial Correlation Regression Spearman Rho Chi-Square Differences Independent t-test Paired t-test 1 way Anova (within & between subjects) Factorial ANOVA Prepared by Dr. Shamala 3 Inferential Statistics – making inferences & generalizations Descriptive Statistics – organise & summarise

Independent t-test 4

Random Sampling 5 Sample 1 Amy Sue Arthur Sample 2 Joe Carol Tim Joe Sue Tim Arthur Amy Carol

Random sampling from pre-existing populations 6 Sample 1 Tim Sam Ken Sample 2 Mary Kay Beth Population 1 Joe Sam Tim Ken Art Harry Will Population 2 Mary Rena Sue Louise Alice Beth Kay

When to use? IV – nominal / categorical variable 2 groups/conditions DV – 1 metric variable (interval / ratio) 7

RQ / Null Hypothesis RQ: Are there any significant differences in psychological therapy (MET & BAS) on weight loss among participants? H 0 :There is no significant differences in psychological therapy (MET & BAS) on weight loss among participants? 8

Assumption for t-test 1.Scale of measurement: IV – nominal scale; DV – metric scale 2. Random sampling 3. Normally distributed (DV) 4. Sample size - typically greater or equal to 30 cases (Refer to Campbell & Stanley, Experimental and Quasi-Experimental Designs for Research) 5. Homogeneity (similarity) of variance (Are the spread of scores (SD) of the two groups pretty close to equal?) 9

H 0 : There are no significant differences between the variances of the 2 groups at.05 level of significance. p >  = do not reject H 0, p <  = reject H0 E.g..078 >.05  there is no sig. diff in variance between the 2 groups. So, EQUAL VARIANCE/ HOMOGENEOUS are assumed. 10 Interpretation of Levene’s Test

Interpretation of Levene’s Test (cont’d).012 <.05  there is a sig. diff between the 2 groups (Don’t Panic, Use UNEQUAL VARIANCE/HETEROGENEOUS) SPSS provides you with an alternative t-value which compensates for the fact that your variances are not the same (Tabachnick and Fidell, 2014). 11

SPSS Procedure Analyze – Compare Means – Independent Sample t-test Place ‘Psychological Therapy’ into ‘Grouping Variable’ box – Define Groups – 1, 2 Place ‘Weight Loss’ into ‘Test Variable’ box. OK 12

Descriptive Output of Independent t- test 13

Interpretation of independent sample t-test Homogeneity of variance was tested by using Levene’s test of equality of variances. Non-significant results (p =.702) were obtained for the dependent variable indicating that error variance of each dependent variable is equal across groups. 14

An independent t-test was used to analyze the significant difference between 2 psychological therapies (MET & BAS) on weight loss. MET (M = 2.84, SD = 2.49) and BAS (M = 7.24, SD = 2.86) differed significantly on weight loss, t (98) = , p =.000. In conclusion, Behavioural Activation System therapy assisted in weight loss among obese participants. 15

PAIRED t-TEST 16

When to use? 2 population means that are correlated. When the sample have: A.pre and post conditions - metric variable (interval / ratio) B.Treatment 1 & Treatment 2 - metric variable (interval / ratio) A.matched pairs - metric variable (interval / ratio) 17

Sampling and Research Design A (pre-test & post-test) 18 Available Subjects Joe Tom Amy Jack Penny Sue David Tim Carol Sample 1 Joe Amy Sue Tim Carol Sample 1 Joe Amy Sue Tim Carol IV / Treatment/ Intervention

Sampling and Research Design B (2 conditions / treatments) 19 Available Subjects Joe Tom Amy Jack Penny Sue David Tim Carol Sample 1 Joe Amy Sue Tim Carol Sample 1 Joe Amy Sue Tim Carol IV 1 / Treatment 1/ Intervention 1 IV 2 / Treatment 2/ Intervention 2 WARNING : CARRY OVER EFFECT!!!

20 Matching Subjects From 2 Populations Sampling and Research Design C (Matching)

Assumptions for paired sample t-test (Dependent Samples t-test) The participants are repeated. The pairs should be normally distributed. Sample size (at least 30 cases per group) 21

Hypothesis / Research Question H o - There is no significant difference between before and after psychological therapy on self- worth among obese participants. RQ - Is there a significant difference between before and after psychological therapy on self- worth among obese participants. 22

SPSS Procedure Analyze – Compare Means – Paired Sample t- test Place the ‘pre-test before therapy & post-test after therapy‘ into ‘Paired Variable’ box OK 23

Output of paired sample t-test 24

Interpretation of t-test Results of a paired sample t-test indicates that there is a statistically significant difference between before and after the psychological therapies on self-worth, t (99) = , p =.000. Participants performed better (M after = 60.06, SD = 14.83) after the treatment of a psychological therapy than before the therapy (M before = 50.05, SD = 17.37). It is concluded that the psychological therapy is effective in increasing the self-worth among obese participants. 25

Distinguishing Between Independent and Correlated Data Sets 26 Flowchart for deciding whether samples are independent or paired.

Analysis of Variance One way ANOVAFactorial ANOVA One Independent Variable More than One Independent Variable Two wayThree way Four way Between subjects Repeated measures / Within subjects Different participants Same participants 27

28 One Way ANOVA (Between Subjects)

When to use? IV – nominal / categorical variable DV – metric variable (interval / ratio) 29

Assumptions Observations derived from random sample. DV must be normally distributed for each group of IV. However, this assumption may be violated with large sample size & can still generate a valid result (Green, 2000). Variances for the groups must be equal (homogenous). 30

Null Hypothesis / RQ H 0 - There is no significant difference in emotional status across ethnicities among obese participants. RQ - Is there a significant difference in emotional status across ethnicities among obese participants? 31

SPSS Procedure Analyze – Compare Means – One-way ANOVA Place ‘Emotional Status’ into ‘Dependent List’ box. Place ‘Ethnicities’ into ‘Factor’ Box. Option – Check ‘Homogeneity of variance test’ Post Hoc – Tukey (to identify pair of groups that are sig different) 32

Levene’s Test 33 Levene’s test shows that all 4 ethnicities have met the assumption of Homogeneity of variance.

Output & Interpretation of 1-way Anova Result revealed a significant difference in emotional status across different ethnicities among obese people, F (3,96) = 2.949, p = SSB SSW SST K-1 N-K N-1 MSB MSW

Post Hoc 35

Interpretation of Post Hoc We can conclude that there is a statistically significant difference between ethnicities, since the significant value in emotional status between Malays and Indians are p =.006. The mean difference between Malays and Indians are (M = 6.745) favouring the Malays. In conclusion, Malay obese people are more emotionally stable compared to Indians. 36

One Way ANOVA Repeated Measures (Within Subjects)

One Way Repeated Measures ANOVA ● Use in experiment in which the same subject is measured under all levels of one or more independent variables ● IV is referred to as repeated-measure factor or within- subjects factor Criteria: 1. Groups must be related (different conditions or at different times). 2. Same participants (within subjects) in each group. 3. The DV must be interval or ratio. Similar to the paired samples T-Test 38

Example o Longitudinal study of annual growth of children over the first five years of life. o The measurement of depression before therapy, after therapy and at a nine month follow up. 39

Time ATime BTime C Repeated Measures ANOVA 40

Assumptions 1DV is normally distributed for each level of the within-subjects factor. 2Sphericity or homogeneity of variance of differences. 3Participants - random samples from the populations. 41

Testing Sphericity Mauchly’s Test If p >.05, assume equality of variances If p <.05, then the data fails to meet the assumption of sphericity Need to use one of the correction factors Greenhouse-Geisser 42

Worked E.g. In a study to determine the effectiveness of exercise techniques in weight loss over months. Obese participants were selected at random. Data for the 1 st month was based on number of exercise training and act as baseline. Weight was taken at 3 rd month and 9 th month. 43

Hypothesis Testing H 0 - There is a significant difference in weight loss across months among obese participants. RQ: Do means on weight loss differ significantly in across months among obese participants? 44

SPSS Procedure 45 Analyze – General Linear Model – Repeated Measures Change ‘factor’ to ‘Months’ Insert Number of levels – 3 – Add – Define Select 3 variables – Within-Subjects Variables Box Options – Select IV (Months) in the Factor and Factor Interactions section and move it into the ‘Display Means’ for box. Tick Compare main effects. Check Descriptive, Estimates of effect size – Continue - OK.

Output 46

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Interpretation A one-way repeated measures ANOVA was conducted to compare scores on weight loss at Month 1 (prior to the exercise intervention), Month 3 (following the intervention) and Month 9 (nine months follow-up). There was a significant effect for months, Wilks’ Lambda =.114, F (2, 98) = , p <.000, multivariate partial eta squared =

Referring to the post hoc test, all results are significant. Comparing the weight loss at the baseline and 9 th month, there is a mean difference 21.29, favouring the 9 th month. In conclusion, the more longer obese participants exercise, the more weight they lose. 50

Factorial Anova (2-way Between Subject Measures)

Also known as two way between subjects ANOVA. A factorial combination of two IVs. Interval/Ratio scale – 1 DV Nominal scale – IV > 2 Factorial ANOVA 52

E.g. of Factorial ANOVA IV 1 – Therapies (MET & BAS) IV 2 – Social Support (Parental & Friend Support) DV – Body Image 53

Assumptions 1. DV is normally distributed for each of levels of the factors. However with moderate to large sample sizes, a skewed distribution may still yield a reasonably accurate results. 2. Population variances of the DV are the same for all levels of IV/factors. 3. Random samples and the scores on the DV are independent of each other. 54

Main Effects and Interaction Effect Main effects: comparing the means of 2 levels (MET and BAS) and Social Support (Parents and Friends). Each IV has its own main effect. Interaction effect: the effect associated with the various combinations of two IVs (Therapies & Social Support towards Body Image). 55

RQ H o 1: There is no significant main effects for IV1 (psychological therapies) on DV (Body Image). H 0 2: There is no significant main effects for IV 2 (Social Support) on DV (Body Image). H O 3: There is no significant interaction effects of psychological therapies and Social Support on Body Image (DV). 56

SPSS Procedure Analyse – GLM – Univariate Body Image – ‘Dependent Variable box’ and Social Support and Psychological therapy into ‘Fixed factor box’ Plot – any IV – horizontal and separate lines – Add, Continue. Option - Highlight all 3 variables from ‘Factor and factor interaction’ box – place into ‘display means box’. Check Descriptive statistics, Estimates of effect size, observed power, homogeneity. 57

Univariate Analysis of Variance 58

It is not significant, which means assumption of homogeneity of variance is fulfilled. 59

The interaction effect is significant 60

Non-parallel graph 61

Interpretation A study was done to examine the influence of psychological therapies and social support on body image. The two-way analysis of variance indicated insignificant main effects for therapies F (1, 95) =.725, p >.397, η2 =.008 ; social support, F (1, 95) =.005, p >.941, η2 =

However, there is a significant interaction effect on therapies and social support, F (1, 95) = 8.155, p <.005, η2 =.079. In conclusion, referring to the graph, when friend’s support is present in Behavioural Activation System therapy, then Body Image is inflated. When parental support exist in Motivational Enhancement therapy, Body Image escalates. WHY??? (Explain based on the theories in Discussion Section) 63

THANK YOU 64