Answers (Chapter 4) - Discovering Statistics Using SPSS:...

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Unformatted text preview: Discovering Statistics Using SPSS: Chapter 4 Chapter 4: Answers Task 1 A student was interested in whether there was a positive relationship between the time spent doing an essay and the mark received. He got 45 of his friends and timed how ling they spent writing an essay (hours) and the percentage they got in the essay (essay). He also translated these grades into their degree classifications (grade): first, upper second, lower second and third class). Using the data are in the file EssayMarks.sav find out what the relationship was between the time spent doing an essay and the eventual mark in terms of percentage and degree class (draw a scatterplot too!). We’re interested in looking at the relationship between hours spent on an essay and the grade obtained. We could simply do a scatterplot of hours spent on the essay (x-axis) and essay mark (y-axis). I’ve also chosen to highlight the degree classification grades using different symbols (just place the variable grades in the style box). The resulting scatterplot should look like this: W 8 0.0 0 Linear Regres sion Grade Essay Mark (%) W 7 0.0 0 W W X X X 6 0.0 0 W W W X X X X X X XX Lower Second Class Third Clas s Essay Mark (%) = 57.93 + 0.66 * hours R-Square = 0.07 X X X X X b Firs t Class Upper Second Class X X X X X W W W W X XX b 5 0.0 0 b 5 .00 1 0.0 0 1 5.0 0 Hours Spent on Essay Next, we should check whether the data are parametric using the explore menu (see chapter 3). The resulting table is as follows: Dr. Andy Field Page 1 4/21/2003 Discovering Statistics Using SPSS: Chapter 4 Tests of Normality a Essay Mark (%) Hours Spent on Essay Kolmogorov-Smirnov Statistic df Sig. .111 45 .200* .091 45 .200* Shapiro-Wilk Statistic df .977 45 .981 45 Sig. .493 .662 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction The K-S and Shapiro-Wilk statistics are both non-significant (Sig. is > .05 in all cases) for both variables which indicates that they are normally distributed. As such we can use Pearson’s correlation coefficient. The result of which is: Correlations Essay Mark (%) Hours Spent on Essay Pearson Correlation Sig. (1-tailed) N Pearson Correlation Sig. (1-tailed) N Essay Mark (%) 1 . 45 .267* .038 45 Hours Spent on Essay .267* .038 45 1 . 45 *. Correlation is significant at the 0.05 level (1-tailed). I chose a 1-tailed test because a specific prediction was made: there would be a positive relationship, that is, the more time you spend on your essay, the better mark you’ll get. This hypothesis is supported because Pearson’s r = .27 (a medium effect size), p < .05, is significant. The second part of the question asks us to do the same analysis but when the percentages are recoded into degree classifications. The degree classifications are ordinal data (not interval): they are ordered categories, so we shouldn’t use Pearson’s test statistic, but Spearman’s and Kendall’s ones instead: Correlations Kendall's tau_b Hours Spent on Essay Grade Spearman's rho Hours Spent on Essay Grade Dr. Andy Field Correlation Coefficient Sig. (1-tailed) N Correlation Coefficient Sig. (1-tailed) N Correlation Coefficient Sig. (1-tailed) N Correlation Coefficient Sig. (1-tailed) N Page 2 Hours Spent on Essay 1.000 . 45 -.158 .089 45 1.000 . 45 -.193 .102 45 Grade -.158 .089 45 1.000 . 45 -.193 .102 45 1.000 . 45 4/21/2003 Discovering Statistics Using SPSS: Chapter 4 In both cases the correlation is non-significant. There was no significant relationship between degree grade classification for an essay and the time spent doing it, ρ = –.19, ns, and τ = – .16, ns. Note that the direction of the relationship has reversed. This has happened because the essay marks were recoded as 1 (first), 2 (upper second), 3 (lower second),and 4 (third) and so high grades were represented by low numbers! This illustrates one of the benefits of NOT taking continuous data (like percentages) and transforming them into categorical data: when you do, you lose information and often statistical power! Task 2 Using the ChickFlick.sav data from Chapter 3, is there a relationship between gender and arousal? Using the same data, is there a relationship between the film watched and arousal? Now, both gender and the film watched are categorical variables with two categories. Therefore, we need to look at this relationship using a point-biserial correlation. The resulting tables are as follows: Correlations Gender Gender Arousal Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N 1 . 40 -.180 .266 40 Arousal -.180 .266 40 1 . 40 Correlations Film Film Arousal Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N 1 . 40 .638** .000 40 Arousal .638** .000 40 1 . 40 **. Correlation is significant at the 0.01 level (2 il d) In both cases I used a 2-tailed test because no prediction was made. As you can see there was no significant relationship between gender and arousal, rpb = –.18, ns. However, there was a significant relationship between the film watched and arousal, rpb = –.64, p < .001. Looking at how the groups were coded, you should see that Bridget Jones’ Diary had a code of 1, and Momento had a code of 2, therefore, this result reflects the fact that as film goes up (changes from 1 to 2) arousal goes up. Put another way, as the film changes from Bridget Jones’ Diary to Momento, arousal increases. So, Momento gave rise to the greater arousal levels. Dr. Andy Field Page 3 4/21/2003 ...
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