Miller_U5

Bias by John Gregory Miller Capella University Presented in Partial Fulfillment Of the Requirements, of BMGT8034: Quantitative Research Techniques 503 Lafayette Street Pittsburg, TX, 75686 Telephone: 903-399-6100 Email: jmiller316@capellauniversity.edu Instructor: Dr. Brock Boudreau

Task 2 - Compute and interpret the descriptive statistics: Statistics Percentage on SPSS exam Computer literacy Percentage of lectures attended Numeracy N Valid 100 100 100 100 Missing 0 0 0 0 Mean 58.10 50.71 59.765 4.85 Median 60.00 51.50 62.000 4.00 Mode 72 a 54 48.5 a 4 Std. Deviation 21.316 8.260 21.6848 2.706 Variance 454.354 68.228 470.230 7.321 Skewness -.107 -.174 -.422 .961 Std. Error of Skewness .241 .241 .241 .241 Kurtosis -1.105 .364 -.179 .946 Std. Error of Kurtosis .478 .478 .478 .478 Range 84 46 92.0 13 Percentiles 25 38.00 45.25 46.125 3.00 50 60.00 51.50 62.000 4.00 75 75.00 56.00 74.875 7.00 a. Multiple modes exist. The smallest value is shown The output shows the table of descriptive statistics for the four variables in this example which are: Percentage on SPSS exam ( M = 58.10, SD = 21.316), Computer literacy ( M = 50.71, SD = 8.260), Percentage of lectures attended ( M = 59.765, SD = 21.6848). From these results we see that, on average, students attended nearly 60% of lectures, obtained 58% in their SPSS exam, scored only 51% on the computer literacy test, and only 5 out of 15 on the numeracy test. In addition, we can see that the standard deviation for computer literacy was relatively insignificant compared to that of the percentage of lectures attended and exam scores. These latter two variables had several modes (multimodal) as shown in the charts below.

Task 7 - Test for Normality, Compute and Interpret a K-S Test: Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig. Percentage on SPSS exam .102 100 .012 .961 100 .005 Numeracy .153 100 .000 .924 100 .000 a. Lilliefors Significance Correction In the data presented here the Percentages on SPSS exam, D (100) = .10, p < .05; and the Numeracy D (100) = 0.15, p < .001, which means that they were both significantly non-normal.

Because of the previous information we have seen that the data from both variables analyzed were not normal, and these plots confirm this observation because the dots deviate substantially from the line. Field (2013) states that on a “Q-Q plot, if values fall on the diagonal of the plot then the variable shares the same distribution as the one specified” (p. 824) . He goes on to say, that deviations will show up when dots fall outside the line (Field, 2013) . One thin to note in this data is that the deviation is greater for the numeracy scores and this is consistent with the higher significance value of this variable on the K-S test.

This shows that there are three cases that fell outside the normal data stream. SPSS makes a distinction for outliers that are more than 1.5 box lengths from one hinge of the box will show up using a circle in the chart. To handle these outliers, I created a Save Standardized Values as Variable for each one of the two variables: Computer Literacy and Numeracy. After that I created a filter for the data set to exclude these from the results. The filter created was: Znumeracy > -3.29 and Znumeracy < 2.63 and Zcomputer >= -2.9. This resulted in the exclusion of four rows of data as seen below: Once the data was excluded the outliers no longer showed in the diagrams for the data as seen below:

Skewness .309 .337 Kurtosis -.567 .662 Sussex University Mean 76.02 1.443 95% Confidence Interval for Mean Lower Bound 73.12 Upper Bound 78.92 5% Trimmed Mean 75.86 Median 75.00 Variance 104.142 Std. Deviation 10.205 Minimum 56 Maximum 99 Range 43 Interquartile Range 12 Skewness .272 .337 Kurtosis -.264 .662 Numeracy Duncetown University Mean 4.12 .292 95% Confidence Interval for Mean Lower Bound 3.53 Upper Bound 4.71 5% Trimmed Mean 4.06 Median 4.00 Variance 4.271 Std. Deviation 2.067 Minimum 1 Maximum 9 Range 8

Interquartile Range 3 Skewness .512 .337 Kurtosis -.484 .662 Sussex University Mean 5.58 .434 95% Confidence Interval for Mean Lower Bound 4.71 Upper Bound 6.45 5% Trimmed Mean 5.38 Median 5.00 Variance 9.432 Std. Deviation 3.071 Minimum 1 Maximum 14 Range 13 Interquartile Range 5 Skewness .793 .337 Kurtosis .260 .662 The variance can also be calculated for the SPSS exam scores the variance ratio is 158.48/104.14 = 1.52 and for numeracy scores the value is 9.43/4.27 = 2.21. These ratios concur with Levene’s test, where the variance for numeracy scores of 2.21 is bigger that the SPSS exam scores of 1.52. References Field, A. (2013). Discovering Statistics using IBM SPSS Statistics, 4th Edition . Sage Publications (UK), 41298.