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MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
MANOVA (July 2014 updated)
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MANOVA (July 2014 updated)

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  • 1. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 1 QUANTITATIVE RESEARCH METHODS SAMPLE OF ANOVA-BASED PROCEDURES Prepared by Michael Ling
  • 2. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 2 Problem A consultant that develops training courses for users of a particular software wants to examine how different characteristics of training courses influence knowledge gained about the software. Specifically, the consultant is interested in the effects of two variables—(i) mode of delivery (face-to-face training versus video-based training) and (ii) the provision of summary notes (provided versus not provided) on knowledge about the software. The consultant recruits 160 individuals to participate in an experiment designed to examine this issue. First, the consultant administers an intelligence (IQ) test to each participant as intelligence is a factor that is known to influence how much knowledge individuals gain from training courses. Each participant is then randomly allocated to one of four conditions (cells) that are formed by crossing the two levels of the mode of delivery factor (i.e., whether the person gets face- to-face training or video training; labelled “face-to-face” versus “video”) with the two levels of the provision of summary notes factor (i.e., whether the person is provided with summary notes or not; labelled “notes” versus “no notes”). The four conditions differ in the following way: 1. In the face-to-face/notes condition, participants spend three hours with an instructor who trains them on how to use the software and then they receive notes that summarise the main points. 2. In the video/notes condition, participants spend three hours watching a video that trains them how to use the software and then they receive notes that summarise the main points. 3. In the face-to-face/ no notes condition, participants spend three hours with an instructor who trains them how to use the software however they do not receive any notes. 4. In the video/ no notes condition, participants spend three hours watching a video that trains them how to use the software however they do not receive any notes. The day following training each participant completes a knowledge test that assesses their knowledge of how to use the software. Dataset The data from the experiment has been entered into the SPSS file SoftTrain.sav. The file contains the following variables:  id = A code used to identify each participant  knowledge = The participants score on the knowledge test completed after training (out of 50).  mode_of_delivery = The mode of delivery condition that the participant was in; video = 0, face-to- face = 1  provision_of_notes = Whether the participant received summary notes; no notes = 0, notes = 1  IQ = The participants score on the intelligence test completed prior to training (out of 1000).
  • 3. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 3 Instructions: The researcher is interested in examining the main effects and interaction effect of mode of delivery and provision of summary notes on knowledge (as measured by the score on the knowledge test). Open the file and conduct the appropriate data analysis. Once you have analysed the data, write a report (no longer than 2-3 double-spaced pages of text with 12pt font) in which you: 1. Describe how you analysed the data 2. Report the results of your data analysis, including an interpretation of what it means. Solution A 2x2 ANOVA/ANCOVA procedure was selected for the analysis because the experiment consisted of (i) two independent factors (‘mode of delivery’ and ‘provision of notes’) each of which had 2 levels and (ii) a single dependent variable (knowledge). In the early stage of our analysis, testing was carried out to find out whether the intelligence (IQ) factor could be considered as a covariate. Testing IQ as a covariate Treating the intelligence factor (IQ) as if it were a covariate, we used the tests of Between-subjects Effects to study any changes in F ratios and error variance (Table 1, 2). We found the total error variance was reduced to 5899.813 from 6081.175, which indicated that IQ was, to a certain extent, related to the dependent variable. However, the F ratios were both reduced for provision of notes (from 22.547 to 20.937) and mode of delivery (from 11.259 to 10.391), which was often an indication that the covariate (IQ) was not only correlated with the dependent variable, but also with the between-groups factors. The covariate (IQ) not only partitioned variance away from the error variance, but also from the variance due to the between- groups factor. By removing the effect of IQ from the analysis, we had removed the true effects of
  • 4. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 4 the between-group factors on the dependent variable. The effect of IQ was not limited to the dependent variable alone. In addition, the relationship between the covariate and the dependent variable was tested and found to be nonlinear, as shown by the scatterplots (Figure 1, 2). The violation of this assumption of ANCOVA reduced the power of the ANCOVA to find significant differences. As a result, the use of IQ as a covariate had been ruled out from subsequent analysis. Testing the basic assumptions of ANOVA Data were analyzed to determine whether the basic assumptions of ANOVA procedure were satisfied. The descriptive statistics were as shown in Table 3. The independence assumption was satisfied as the participants were randomly allocated to one of the four groups. The scale of measurement assumption was satisfied as the dependent variable (knowledge) was an interval score from 0 to 50. As Levene’s Test for equality of error variance was non- significant (Sig > 0.05), thus the assumption of homogeneity of variance had not been violated (Table 4). The skewness and kurtosis of the two groups in the mode of delivery factor were shown in Table 5. Likewise, the skewness and kurtosis of the two groups in the provision of notes factor were shown in Table 6. Their values lied between -1 and +1 which indicated that each of the four groups was approximately normally distributed. This was also supported by the non- significance of the Shapiro-Wilk statistics in the two groups of mode of delivery (Table 7) and the two groups of provision of notes (Table 8). The box plots showed that there were no outliners in the four groups (Figure 3, 4). Normality of the sampling distribution was attained.
  • 5. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 5 Main and interaction effects To investigate the main and interaction effects, we used ANOVA to examine four sources of variability: (i) variability due to main effect of mode of delivery; (ii) variability due to main effect of provision of notes; (iii) variability due to interaction effect of mode of delivery and provision of notes; and (iv) within group (or error) variability. As shown in Table 3, participants provided with notes (n=80, M = 29.3375, SD = 6.31844) achieved significantly higher scores than participants provided with no notes (n=80, M = 24.6500, SD = 6.67908). The main effect of provision of notes factor was statistically significant, F(1, 156) = 22.547, p < .005 (Table 1). Partial eta-square of the provision of notes factor showed that it accounted for 12.6% of the overall variability (Table 1), which was a ‘medium’ effect. As shown in Table 3, participants in face-to-face delivery mode (n=80, M = 28.6500, SD = 6.84937) achieved significantly higher scores than participants in video delivery mode (n=80, M = 25.3375, SD = 6.57179). The main effect of mode of delivery factor was also statistically significant, F(1, 156) = 11.529, p < .05 (Table 1). Partial eta-square of the delivery factor showed that it accounted for 6.7% of the overall variability (Table 1), which was a ‘medium’ effect. The interaction effect of the mode of delivery and the provision of notes was statistically significant, F (1, 156) = 4.053, p < 0.05 (Table 1). Partial eta-square of the interaction effect showed that it accounted for 2.5% of the overall variability (Table 1), which was a ‘small’ effect. Nevertheless, with respect to the effect of mode of delivery on knowledge test, the profile plot showed that it was an ordinal interaction. The mode of delivery had a stronger effect on the knowledge test of the participants when they were not provided with notes than when they were provided with notes (Figure 5).
  • 6. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 6 With respect to the effect of provision of notes on knowledge test, the profile plot showed that it was an ordinal interaction. The provision of notes had a stronger effect on the knowledge test of the participants when they were trained in video mode than when they were trained in face-to-face mode (Figure 6).
  • 7. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 7 Appendix Table 1: Tests of Between-Subjects Effects (with no covariate) Dependent Variable:knowledge test Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Corrected Model 1475.819a 3 491.940 12.620 .000 .195 Intercept 116586.006 1 116586.006 2990.773 .000 .950 provision_of_notes 878.906 1 878.906 22.547 .000 .126 mode_of_delivery 438.906 1 438.906 11.259 .001 .067 provision_of_notes * mode_of_delivery 158.006 1 158.006 4.053 .046 .025 Error 6081.175 156 38.982 Total 124143.000 160 Corrected Total 7556.994 159 a. R Squared = .195 (Adjusted R Squared = .180) Table 2: Tests of Between-Subjects Effects (with IQ as covariate) Dependent Variable:knowledge test Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Corrected Model 1657.180a 4 414.295 10.884 .000 .219 Intercept 1897.936 1 1897.936 49.863 .000 .243 IQ 181.362 1 181.362 4.765 .031 .030 provision_of_notes 796.945 1 796.945 20.937 .000 .119 mode_of_delivery 395.530 1 395.530 10.391 .002 .063 provision_of_notes * mode_of_delivery 203.173 1 203.173 5.338 .022 .033 Error 5899.813 155 38.063 Total 124143.000 160 Corrected Total 7556.994 159 a. R Squared = .219 (Adjusted R Squared = .199)
  • 8. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 8 Table 3: Descriptive Statistics Dependent Variable:knowledge test provision of notes factor mode of delivery factor Mean Std. Deviation N no notes video 22.0000 5.59762 40 face-to-face 27.3000 6.68024 40 Total 24.6500 6.67908 80 notes video 28.6750 5.77078 40 face-to-face 30.0000 6.83130 40 Total 29.3375 6.31844 80 Total video 25.3375 6.57179 80 face-to-face 28.6500 6.84937 80 Total 26.9938 6.89407 160 Table 4: Levene’s Test of Equality of Error Variancea Dependent Variable:knowledge test F df1 df2 Sig. .527 3 156 .664 Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
  • 9. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 9 Table 5: Descriptives of ‘Mode of Delivery’ mode of delivery factor Statistic Std. Error knowledge test video Mean 25.3375 .73475 95% Confidence Interval for Mean Lower Bound 23.8750 Upper Bound 26.8000 5% Trimmed Mean 25.3611 Median 25.0000 Variance 43.188 Std. Deviation 6.57179 Minimum 9.00 Maximum 42.00 Range 33.00 Interquartile Range 8.75 Skewness .075 .269 Kurtosis .026 .532 face-to-face Mean 28.6500 .76578 95% Confidence Interval for Mean Lower Bound 27.1257 Upper Bound 30.1743 5% Trimmed Mean 28.5417 Median 29.0000 Variance 46.914 Std. Deviation 6.84937 Minimum 12.00 Maximum 49.00 Range 37.00 Interquartile Range 9.00 Skewness .181 .269 Kurtosis .427 .532
  • 10. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 10 Table 6: Descriptives of ‘Provision of notes’ provision of notes factor Statistic Std. Error knowledge test no notes Mean 24.6500 .74674 95% Confidence Interval for Mean Lower Bound 23.1636 Upper Bound 26.1364 5% Trimmed Mean 24.5000 Median 24.5000 Variance 44.610 Std. Deviation 6.67908 Minimum 9.00 Maximum 46.00 Range 37.00 Interquartile Range 8.75 Skewness .410 .269 Kurtosis .762 .532 notes Mean 29.3375 .70642 95% Confidence Interval for Mean Lower Bound 27.9314 Upper Bound 30.7436 5% Trimmed Mean 29.3333 Median 29.0000 Variance 39.923 Std. Deviation 6.31844 Minimum 12.00 Maximum 49.00 Range 37.00 Interquartile Range 7.75 Skewness .040 .269 Kurtosis .554 .532
  • 11. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 11 Table 7: Tests of Normality for ‘mode of delivery’ mode of delivery factor Kolmogorov-Smirnova Shapiro-Wilk Statistic df Sig. Statistic df Sig. knowledge test video .100 80 .046 .990 80 .774 face-to-face .059 80 .200* .988 80 .684 a. Lilliefors Significance Correction *. This is a lower bound of the true significance. Table 8: Tests of Normality for ‘provision of notes’ provision of notes factor Kolmogorov-Smirnova Shapiro-Wilk Statistic df Sig. Statistic df Sig. knowledge test no notes .092 80 .094 .983 80 .392 notes .066 80 .200* .990 80 .765 a. Lilliefors Significance Correction *. This is a lower bound of the true significance.
  • 12. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 12 Figure 1: Scatterplot between IQ and Knowledge test; mode of delivery as independent variable Figure 2: Scatterplot between IQ and Knowledge test; provision of notes as independent variable. .
  • 13. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 13 Figure 3: Effect of mode of delivery on knowledge test Figure 4: Effect of provision of notes on knowledge test
  • 14. ANOVA-BASED PROCEDURES July 2014 updated Prepared by Michael Ling Page 14 Figure 5: Effect of mode of delivery on knowledge test Figure 6: Effect of mode of delivery on knowledge test

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