Workshop Research Methods and Statistical Analysis
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1 Workshop Research Methods and Statistical Analysis Session 2 Data Analysis Sandra Poeschl Page 1
2 Research process Research Question State of Research / Theoretical Background Design Data Collection Sampling Operationalization Data Preparation Data Analysis Dissemination
3 Research process Research Subject State of Research / Theoretical Background Design Data Collection Sampling Operationalization Data Preparation Data Analysis Dissemination
4 Designs we will deal with Experimental designs Quantitative Empirical Explanatory Sample study Frequency of measurements as an effect on choice of statistical tests Cross-sectional Repeated measures Page 4
5 Agenda Descriptive and inferential statistics Indication (which test?) Two groups (experimental / control) t-test for independent and dependent samples One-way (1 factor) One-way ANOVA Multi-factorial (several factors) Two-way ANOVA, within-between subjects Page 5
6 DESCRIPTIVE AND INFERENTIAL STATISTICS Page 6
7 Descriptive vs. inferential Descriptive statistics Reporting sample data Measures of location (arithmetic mean, median, mode) Measures of spread (range, variance, standard deviation) Correlations frequencies Reported in text, also tables, graphs Inferential statistics Inference from sample data to population effects Parameter estimation Point & interval estimation Testing hypotheses Significance tests Page 7
8 Descriptive vs. inferential in explanatory studies Descriptive statistics Decribing the sample Complementary presentation of sample statistics for tested hypotheses Inferential statistics Testing hypotheses Significance tests Page 8
9 WHICH TEST? Page 9
10 How do I choose the appropriate test? Type of hypothesis Difference, correlation, change Number of groups / treatments or variables Levels of measurement nominal, ordinal, interval / ratio Page 10
11 Level of measurement Affiliation to Category Nominal + Rank order Ordinal + + Same differences between gradings Interval Absolute zero Ratio Nominal: eye color Ordinal: level of education Interval: opinion, date Ratio: age Page 11
12 TWO GROUPS Page 12
13 2-Groups (Treatment / Control) 1 IV, dichotomous, 1 DV, metric (univariate) Cross-sectional or repeated measures t-test (independent / dependent samples) No sound Spatial sound IV: sound (no sound/spatial sound DV: error rate in an orientation task Page 13
14 Which test? H1: Integrating spatial sound in a VE leads to lower error rates in an orientation task than a nosound display. Hypothesis on a difference Independent samples 1 independent variable, 2 groups (no sound / spatial sound) 1 dependent variable (ratio) Student s t-test Page 14
15 Requirements Student s t-test Level of measurement of DV at least interval Normal distribution of DV Variances σ A and σ B are equal Levene s Test for equality of variances, corrections of df. Sample within groups should be very similar, n A = n B > 30. Non-parametric alternative: Mann-Whitney U- Test Page 15
16 A priori power analysis Test family: t tests Statistical test: Means: Differences between two independent means Type of power analysis: A priori Medium effect size d =.5 α =.05 1-β =.80 Allocation ratio = 1 Sample size / group = 51 Total sample size = Page 16
17 The data set One case per row One variable per column Part = participant # Cond = condition Error = error rate Page 17
18 Independent Samples t-test Analyze / Compare Means / Independent-Samples T Test Page 18
19 Independent Samples t-test Determine Grouping Variable Condition Page 19
20 Page 20 SPSS Output
21 Effect size Test family: t tests Statistical test: Means: Difference between 2 independent means Type of power analysis: post hoc Determine Effect Size (Means, SD) Sample Sizes Page 21
22 Results H1: Integrating spatial sound in a VE leads to lower error rates in an orientation task than a nosound display. M no sound = 4.10 (SD = 1.29; n = 10) M spatial sound = 2.6 (SD = 1.17; n = 10) d = 1.22 (large) t = 2.72; df = 18; p <.05 H 0 is rejected Page 22
23 Which test? H1: Integrating spatial sound in a VE leads to lower error rates in an orientation task than a nosound display. Hypothesis on a difference Dependent samples 1 independent variable, 2 groups (no sound / spatial sound), within-subjects 1 dependent variable (ratio) Student s t-test for paired samples Page 23
24 A priori power analysis Test family: Means: Difference between two dependent means Type of power analysis: A priori Medium effect size d =.5 α =.05 1-β =.80 Total sample size = Page 24
25 Data Set 2 variables / participant: dependent variable for condition 1 and condition Page 25
26 Paired-Samples t-test Analyze / Compare Means / Paired-Samples T-Test Page 26
27 Paired-Samples t-test Determine paired variables Page 27
28 Page 28 SPSS Output
29 Effect size Test family: t tests Statistical test: Means: Difference between 2 dependent means Type of power analysis: post hoc Determine Effect Size (mean and SD of difference) Sample Size Page 29
30 Results H1: Integrating spatial sound in a VE leads to lower error rates in an orientation task than a nosound display. M no sound = 4.19 (SD = 1.28; n = 66) M spatial sound = 3.15 (SD = 1.36; n = 66) d =.92 (large) t = 7.46; df = 65; p <.0001 H 0 is rejected Page 30
31 ONE-WAY (1 FACTOR) Page 31
32 One-way ANOVA One-way, univariate: 1 IV, more than 2 levels (nominal), 1 DV (metric) Cross-sectional or repeated measures One-way, univariate ANOVA (repeated measures) FOR 20 FOR 90 FOR 270 IV: FOR (20 degrees/90 degrees/270 degrees) DV: error rate in search task Page 32
33 Which test? H1: Higher field of regard leads to reduced error rate in a search task. Hypothesis on a difference Independent samples / between-subjects 1 independent variable, 3 groups (FOR 20 / FOR90 / FOR270) 1 dependent variable (ratio) One-way univariate ANOVA Page 33
34 Requirements ANOVA DV = interval / ratio normal distribution for DV N > 20 per cell N max / n min < 1.5 Homogeneity of variances between samples Non-parametric alternative: Kruskal-Wallis-Test Page 34
35 A priori power analysis Test family: F tests Statistical test: ANOVA, fixed effects, omnibus, oneway Type of power analysis: A priori Medium effect size f =.25 α =.05 1-β =.80 Number of groups = 3 Total sample size = Page 35
36 Page 36 Data Set
37 One-way univariate ANOVA Analyze / General Linear Model/ Univariate Page 37
38 One-way univariate ANOVA Determine DV and IV Page 38
39 Post hoc Tests Pick post hoc tests for differences between groups Page 39
40 Options Display: descriptive statistics Estimates of effect size Observed power Homogeneity tests Page 40
41 SPSS Output Descriptive Statistics Page 41
42 SPSS Output Homogeneity Variances should be similar, therefore Levene s Test should show a non-significant result Page 42
43 SPSS Output Between-Subjects Effects Page 43
44 SPSS Output Post hoc Tests Page 44
45 Page 45 Output JMP
46 Results H1: Higher field of regard leads to reduced error rate in a search task. M FOR20 = 3.60 (SD = 1.35; n = 10) M FOR90 = 2.90 (SD = 1.20; n = 10) M FOR270 = 2.00 (SD = 1.15; n = 10) Partial η 2 =.24 (large) F = 4.21; df = 2; p =.026 H 0 is rejected for FOR20 and FOR Page 46
47 MULTI-FACTORIAL, REPEATED MEASURES Page 47
48 Multi-factorial ANOVA Multi-factorial, At least 2 IV, at least 1 DV Cross-sectional or repeated measures Interaction effects No sound first Sound first No sound Spatial Sound IV 1: sound (no sound / spatial sound) IV 2: order of presentation (no sound first / spatial sound first) DV: presence experienced (SUS Mean) Page 48
49 Which test? H1: Integrating spatial sound into a VR scene leads to higher levels of presence experienced than a no sound display. Hypothesis on a difference 1 within-subjects factor (sound), 1 betweensubjects factor (order of presentation) 1 dependent variable (presence experienced, interval) Two-way ANOVA, repeated measures Page 49
50 Requirements ANOVA, Repeated Measurements DV = interval / ratio, normal distribution Complete dataset per participant for several measurements (conditions, points in time) Covariances between different measurements have to be similar (sphericity) Non-parametrical alternative: Friedman-Test Page 50
51 A priori power analysis Test family: F tests Statistical test: ANOVA, repeated measures, within-between interaction Type of power analysis: A priori Medium effect size f=.25 α =.05 1-β =.80 Number of groups = 2 Number of measurements = 2 Total sample size = Page 51
52 Data Set 2 variables / participant: dependent variable for condition 1 and condition Page 52
53 Two-way ANOVA, repeated measures Analyze / General Linear Model / Repeated Measures Page 53
54 Two-way ANOVA, repeated measures Determine withinsubjects factor (sound) and number of levels Determine DV (measure name) Page 54
55 Two-way ANOVA, repeated measures Add DV to analysis (NB: 2 variables!) Determine betweensubjects factor (order of presentation Page 55
56 Two-way ANOVA, repeated measures Check post hoc tests Page 56
57 Two-way ANOVA, repeated measures Display: descriptive statistics for factors and interaction Estimates of effect size Observed power Homogeneity tests Page 57
58 SPSS Output - Factors Page 58
59 SPSS Output Descriptive Statistics Page 59
60 SPSS Output Levene s Test Variances should be similar, therefore Levene s Test should show a non-significant result Page 60
61 SPSS Output - Sphericity Page 61
62 SPSS Output within-subjects effects Page 62
63 SPSS Output Between- Subjects Effects Page 63
64 Results H1: Integrating spatial sound into a VR scene leads to higher levels of presence experienced than a no sound display. M no sound = 3.15 (SD = 1.36; n = 66) M sound = 4.19 (SD = 1.28; n = 66) Partial η 2 =.46 (large) F = 55.12; df = 1; p =.002 H 0 is rejected Page 64
65 Further Reading Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics.(4 th ed.).thousand Oaks: Sage Publications Howell, D. (2012). Statistical Methods for Psychology. (8 th ed.). Cengage Learning Emea Marques de Sá, J. P. (2007). Applied Statistics Using SPSS, STATISTICA, MATLAB and R. (2 nd ed.) Berlin: Springer Page 65
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