Causality and Inferences: Structuring the Well-formed Hypothesis - Assignment Example

Causality and Inferences: Structuring the Well-formed Hypothesis Part 1 Bryant in his article reported conclusion on CEOs golf handicap of 44 cases from the 51 in the data set. Bryan identified 11 low performing companies, 22 middle performing companies, and 11 high-performing companies. Further, Bryan calculated the mean golf handicap of the CEOs running these companies for each of the three groups; and checked whether the differences between these means are sufficiently great. However, Bryan had not reported the criterion by which he had excluded seven of the cases from 51 cases. This report will try to analyze the same procedure as Bryan employed and will select three groups based on stock rate as 11 low performing companies (Group 1), 22 middle performing companies (Group 2), and 11 high-performing companies (Group 3). First, confidence interval will be calculated to check differences between three groups and then T-tests will be performed on pair of groups to check whether there is difference in CEOs golf handicap for low, middle, and high performing companies. Further, this report will check whether there is association between region (East, South, Midwest, and West) and survivor (company independently exist in 2006 or not). The average CEOs golf handicap was 15.45 (SD = 6.02). About half of the CEOs golf handicap was below 15. The range of the CEOs golf handicap was 31 with minimum and maximum CEOs golf handicap was 3 and 34, respectively. The distribution of the CEOs golf handicap was approximately normally distributed (Table 1). The average stock rate of the companies was 52.47 (SD = 25.15). About half of the company’s stock rate was below 49. The range of stock rate of the companies was 94 with minimum and maximum stock rate of the companies was 3 and 97, respectively. The distribution of the CEOs golf handicap was normally distributed (Table 1). Table 1: Descriptive Statistics handicap stockrate N Valid 51 51 Missing 0 0 Mean 15.45 52.47 Median 15.00 49.00 Mode 13 22(a) Std. Deviation 6.021 25.149 Skewness .525 .088 Std. Error of Skewness .333 .333 Range 31 94 Minimum 3 3 Maximum 34 97 Percentiles 25 11.00 33.00 50 15.00 49.00 75 19.00 74.00 a Multiple modes exist. The smallest value is shown From table 1, it can be seen that about 25% companies had stock rate up to 33, about 50% companies had stock rate from 34 to 74 and remaining 25% companies had stock rate above 74. Therefore, initially, three stock rate groups are divided based on percentiles of stock rate. Than odd values from each group are removed and some values are moved to another group so that three groups as 11 low performing companies (Group 1), 22 middle performing companies (Group 2), and 11 high-performing companies (Group 3) are formed. The average CEOs golf handicap of low performing companies (Group 1) was 17.91 (SD = 3.24). The average CEOs golf handicap of middle performing companies (Group 2) was 14.73 (SD = 4.64). The average CEOs golf handicap of high performing companies (Group 1) was 13.27 (SD = 6.81). The overall average CEOs golf handicap of 44 selected cases was 15.16 (SD = 5.17) (Table 2). From table 1, it appears that the average golf handicap was decreasing from low to high performing companies; however, there is more variation in the golf handicap from low to high performing companies. Table 2: Mean Golf Handicap Comparison of Three Groups Group Mean N Std. Deviation Group 1 17.91 11 3.239 Group 2 14.73 22 4.641 Group 3 13.27 11 6.813 Total 15.16 44 5.167 Confidence Interval Figure 1: 95% Confidence Interval of CEOs Golf Handicap of Three Groups Figure 1 shows the 95% Confidence Interval graphs for the three groups. From, figure 1, it can be seen that the intervals for three groups overlap with each other that suggest the differences between groups means are not sufficiently great. T-tests Group 1 and Group 2 The differences between Group 1 and Group 2 CEOs mean golf handicap is not significant, t(31) = 2.03, p = .051. Table 3: Group Statistics group N Mean Std. Deviation Std. Error Mean handicap Group 1 11 17.91 3.239 .977 Group 2 22 14.73 4.641 .990 Table 4: Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper handicap Equal variances assumed 2.538 .121 2.032 31 .051 3.182 1.566 -.011 6.375 Equal variances not assumed 2.289 27.35 .030 3.182 1.390 .331 6.033 Group 1 and Group 3: The differences between Group 1 and Group 3 CEOs mean golf handicap is not significant, t(20) = 2.04, p = .060. Table 5: Group Statistics group N Mean Std. Deviation Std. Error Mean handicap Group 1 11 17.91 3.239 .977 Group 3 11 13.27 6.813 2.054 Table 6: Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper handicap Equal variances assumed 8.960 .007 2.038 20 .055 4.636 2.275 -.108 9.381 Equal variances not assumed 2.038 14.30 .060 4.636 2.275 -.232 9.505 Group 2 and Group 3: The differences between Group 1 and Group 2 CEOs mean golf handicap is not significant, t(31) = 0.72, p = .474. Table 7: Group Statistics group N Mean Std. Deviation Std. Error Mean handicap Group 2 22 14.73 4.641 .990 Group 3 11 13.27 6.813 2.054 Table 8: Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper handicap Equal variances assumed 3.754 .062 .724 31 .474 1.455 2.008 -2.641 5.550 Equal variances not assumed .638 14.80 .533 1.455 2.280 -3.411 6.320 In conclusion, 95% confidence interval and T-tests for pair of groups suggest that there is no difference in CEOs mean golf handicap for low, middle and high performing companies. Crosstab There is no relationship between region and survivor, χ2(3, N = 44) = 0.54, p = .91. Tau-B is not significant either, Tau-B = 0.028, p = .847. In other words, there is no support for a hypothesis that region and survivor are interdependent. Table 9: Crosstab of Region and Survivor survivor Total Not Independent Existence in 2006 Independent Existence in 2006 Region East Count 8 12 20 Expected Count 7.3 12.7 20.0 % within Region 40.0% 60.0% 100.0% % within survivor 50.0% 42.9% 45.5% Std. Residual .3 -.2 Midwest Count 3 8 11 Expected Count 4.0 7.0 11.0 % within Region 27.3% 72.7% 100.0% % within survivor 18.8% 28.6% 25.0% Std. Residual -.5 .4 South Count 3 5 8 Expected Count 2.9 5.1 8.0 % within Region 37.5% 62.5% 100.0% % within survivor 18.8% 17.9% 18.2% Std. Residual .1 .0 West Count 2 3 5 Expected Count 1.8 3.2 5.0 % within Region 40.0% 60.0% 100.0% % within survivor 12.5% 10.7% 11.4% Std. Residual .1 -.1 Total Count 16 28 44 Expected Count 16.0 28.0 44.0 % within Region 36.4% 63.6% 100.0% % within survivor 100.0% 100.0% 100.0% Table 10: Chi-Square Tests Value df Asymp. Sig. (2-sided) Pearson Chi-Square .540(a) 3 .910 Likelihood Ratio .556 3 .906 N of Valid Cases 44 a 4 cells (50.0%) have expected count less than 5. The minimum expected count is 1.82. Table 11: Symmetric Measures Value Asymp. Std. Error(a) Approx. T(b) Approx. Sig. Ordinal by Ordinal Kendall's tau-b .028 .142 .193 .847 N of Valid Cases 44 a Not assuming the null hypothesis. b Using the asymptotic standard error assuming the null hypothesis. Additional Analysis (One Sample T-test) The one-sample T-test will be conducted to test whether CEOs mean golf handicap was equal to 15. The CEOs mean golf handicap was equal to 15, t(50) = 0.54, p = .595. In other words, there is support for a hypothesis that the CEOs mean golf handicap was equal to 15. Table 12: One-Sample Statistics N Mean Std. Deviation Std. Error Mean handicap 51 15.45 6.021 .843 Table 13: One-Sample Test Test Value = 15 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper handicap .535 50 .595 .451 -1.24 2.14 Part 2—Optional Extra Credit The companies can be divided in many sectors. In this part, it will be analyzed whether there is difference between CEOs golf handicap based on company sector. Table 14, summarizes the CEOs golf handicap based on company sector. The mean CEOs golf handicap for different sectors is from 11 to 18. Most of the mean CEOs golf handicap for different sector of companies is around 14-15. Figure 2 shows the 95% Confidence Interval of CEOs golf handicap of different sector for companies. From, figure 2, it can be seen that the intervals for all sectors overlap with each other that suggest the differences between mean CEOs golf handicap based on company sector are not sufficiently great. Table 14: Descriptive Statistics of CEOs Golf Handicap Based on Sector Sector Name N Mean Median Std. Deviation Maximum Minimum Range Skewness 70 14.046 13.450 5.3777 29.0 2.5 26.5 .442 Consumer Discretionary 27 13.307 14.700 5.7877 28.8 4.4 24.4 .757 Consumer Staples 14 16.357 15.150 6.3542 26.2 8.5 17.7 .482 Energy 8 17.638 17.400 6.6967 26.6 9.2 17.4 .166 Financials 33 13.545 13.000 5.8064 27.5 2.4 25.1 .334 Health Care 15 14.693 14.800 6.6077 25.7 4.8 20.9 .092 Industrials 22 15.655 16.100 4.5759 24.5 6.5 18.0 -.281 Information Technology 19 14.521 14.800 5.0942 21.4 2.9 18.5 -.639 Materials 8 12.125 13.050 4.9158 18.6 5.7 12.9 -.116 Telecommunication Services 3 10.833 11.100 3.4078 14.1 7.3 6.8 -.350 Utilities 13 15.177 14.500 5.5981 26.5 5.4 21.1 .515 Total 232 14.341 14.150 5.5813 29.0 2.4 26.6 .318 Figure 2: 95% Confidence Interval of CEOs Golf Handicap of Different Sector Read More