A Toolkit for Quantitative Data Analysis - Assignment Example

Quantitative analysis data using SPSS Name: Course: Instructor: Date: QUESTION 1 a. Mean and standard deviation of the two areas for Family IQ score. Statistics Combined family IQ score N Valid 100 Missing 0 Mean 549.86 Std. Error of Mean 6.911 Median 543.50 Std. Deviation 69.110 Variance 4776.223 Skewness .324 Std. Error of Skewness .241 Kurtosis -.112 Std. Error of Kurtosis .478 Suburb Frequency Percent Valid Percent Cumulative Percent Valid Western suburbs 50 50.0 50.0 50.0 Eastern suburbs 50 50.0 50.0 100.0 Total 100 100.0 100.0 b. The appropriate assumptions on the FamilyIQ data and report your findings The study wanted to assess where the smart people lived in Melbourne. In try to undertake study, a sample of 50 households were surveyed in two different areas. That is; east and west side of Melbourne. Each household had to report their combined family IQ score. It is worth noting that a total of 5 individuals were sampled from each household their sum IQ representing the FamilyIQ for that household. The assumption of the study is: The smarter people lived on the western suburbs Points to note: 1=Western suburbs 2=Eastern suburbs Results Case Processing Summary Cases Included Excluded Total N Percent N Percent N Percent Combined family IQ score * Suburb 100 100.0% 0 0.0% 100 100.0% Case Summaries Combined family IQ score Suburb N Mean Median Range Std. Deviation Variance Std. Error of Mean Western suburbs 50 564.24 564.50 324 68.478 4689.247 9.684 Eastern suburbs 50 535.48 522.00 342 67.370 4538.663 9.528 Total 100 549.86 543.50 342 69.110 4776.223 6.911 According to the results above, the mean FamilyIQ for Eastern and Western suburbs are 535.48 and 564.24 respectively. In this regard, people living in western suburbs have higher FamilyIQ as compared to the western suburbs. Therefore, the assumption that western people are smarter than their eastern counterparts is valid. c. Is there a significant difference between the two areas of Melbourne for IQ score? The hypothesis: Ho: there a significant difference between the two areas of Melbourne for IQ score Ha: there no significant difference between the two areas of Melbourne for IQ score One way Anova ANOVA Suburb Sum of Squares df Mean Square F Sig. Between Groups 19.333 81 .239 .758 .801 Within Groups 5.667 18 .315 Total 25.000 99 The confidence level of the study is 95% hence the significance=0.05. From the ANOVA results above, the P-value is 0.801. The significance level (0.05)p-value (0.00) therefore we accept the null hypothesis that a mean difference of 23.4 shows a significant increase in IQ scores over the 12 week period. Hence, there is a significant increase of IQ scores over the 12 weeks of experiments. c) Effect size of the data The effect size is a quantitative measure of the strength of a phenomenon. The effect size measures include correlation between two variables, the regression coefficient, the mean difference and many more. For every effect-size, a larger absolute value always indicates a stronger effect. It is worth noting that effect sizes analysis complement statistical hypothesis testing and is vital in statistical power analysis. The effect size Cohen’s formula is given by Cohen’s d formula However, this study will use correlation to determine the effect size of the study. Correlation results Paired Samples Correlations N Correlation Sig. Pair 1 pre semester IQ score & post semester IQ scores 20 -.015 .949 The correlation coefficient shows a negative correlation between the two variables. That is, the pre-test and the post-test are negatively related. The correlation results complement the hypothesis testing above and proves that there is a significance increase in the IQ score. This is because, post-scores are higher than the pre-score hence the negative correlation. d) What conclusions can be drawn from this output regarding the value of teaching students to think? The results shows that there is an improvement in thinking as a result of experimental teaching method. That is, after the 12 weeks of study, the students were characterized by high IQ scores as opposed to low IQ scores prior to the study. Therefore, it is prudent to conclude that the new experimental teaching method (i.e. encouraging students to think) was beneficial. e) What is the research hypothesis for this study? Indicate the dependent variable and the independent variable The research hypothesis of the study is: H0: The new experimental teaching method (i.e. encouraging students to think) was beneficial. H1: The new experimental teaching method (i.e. encouraging students to think) was not beneficial. The dependent variable of the study was IQ score while the independent variable was new experimental teaching method. QUESTION 3 i. Assumptions The study was investigating how long it took students to get to VU St Albans from VU City campus each day via public transport. However, in so doing, the study assumes that all the students come from totally different locations and they all use public transport when going to campus. ii. Does the time it takes to get to university improve over time? Descriptive Statistics control or experimental Mean Std. Deviation N pre intervention time in minutes experimental group 45.75 2.500 4 control group 39.00 3.916 4 Total 42.38 4.719 8 post intervention time in minutes experimental group 40.00 4.761 4 control group 40.50 3.873 4 Total 40.25 4.027 8 follow up time in minutes experimental group 30.75 2.986 4 control group 40.00 4.082 4 Total 35.38 5.951 8 From the statistics above, the mean time for arriving at school for experimental group are 45.75, 40.00 and 30.75 for pretest, posttest and follow-up respectively. This shows that there is an improvement in the time for arriving at school. The means for control group are 39, 40.50, and 40.0 for pretest, posttest and follow-up respectively. However, the total time for pre-intervention, post intervention and follow-up are 42.38, 40.25 and 35.38 that show an improvement in time. iii. Is the experimental group better than the control group at getting to university? To achieve this answer, the hypothesis that the observed covariance matrices of the dependent variables are equal across groups as shown below. Box's Test of Equality of Covariance Matricesa Box's M 11.354 F .824 df1 6 df2 260.830 Sig. .552 Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups. a. Design: Intercept + group Within Subjects Design: time According to Box's Test of Equality of Covariance Matrices, the p-value is given by 0.552. The significance level (0.05) Read More