Statistical Analysis of the Missing Values - Assignment Example

Course Assignment 3 A. Outliers 1. Unless one employs a systematic way of managing missing data, the missing values bias statistical analysis because they are treated as zero. In the most basic example, calculating for the mean without making special provisions for missing values (such as using a spreadsheet function that discounts missing values or sorting the data column and running a calculation only on the non-zero cells) will yield an average that is lower than it should be. A second example that applies is a correlation where the missing values would similarly enter the equation as zeroes and therefore distort the analysis. 2. Two ways of isolating the missing data items is by visual inspection with the help of the End-DOWN navigation key and employing a series of sorts. The resulting lists are as follows: VARIABLES MISSING CASES Yrsserv # 66 Edlevel #s 9, 18, 88, 106, 117, 129, 160, 164, 189, 190, 226, 250, 263, 271, 277, 283, 297, 310, 318, 320, 324, 342, 344, 348, 371, 373, 397, Basic03 14, 26, 28, 35, 50, 80, 84, 120, 130, 134, 139, 175, 229, 231, 257, 280, 281, 296, 315, 336, 352 Bonus03 Exactly the same as for Basic03: 14, 26, 28, 35, 50, 80, 84, 120, 130, 134, 139, 175, 229, 231, 257, 280, 281, 296, 315, 336, 352 Output03 Two more than Basic 03 and Bonus03: 14, 26, 28, 35, 50, 80, 84, 120, 130, 134, 139, 158, 175, 229, 231, 257, 280, 281, 296, 315, 336, 352, 379 Output04 158, 379 3. The scatter diagrams of the pay data, variables Basic03 and Basic04, are shown below. Figure 1 4. In both months, the outliers are case numbers 158 and 379. Figure 2 5. These two cases are defined as outliers because visual inspection reveals that they are several multiples of the standard deviation removed from the base pay range that accounts for 99.5% of all cases. 6. It is highly probable that cases 158 and 379 are managers only because their base pay are more than twice the highest base pay levels of everybody else. Otherwise, there is no telling from their age or educational qualifications. B. Mean Pay for Men and Women 1. The null hypothesis is stated as follows: “There is no difference in mean pay between men and women” Or, in symbolic form: Basic04M = Basic04F. 2. The alternative hypothesis: “Mean pay for men is higher than for women” Or, in symbolic form: Basic04M > Basic04F. 3. Stated this way, it is a two-tailed formulation. 4. Applying the Excel function of an F Test on Two Samples for Variance (after, of course, transforming the gender labels from text to numeric data with an IF function), we obtain the result: Table 1 F-Test Two-Sample for Variances   Gender2 Basic04 Mean 1.38 1289.325 Variance 0.23619 145573.7 Observations 400 400 df 399 399 F 1.62E-06 P(F Read More