# HLT362V Applied Statistic For Health Care Professionals

Pages: 4 Words: 890

## Question:

How would you characterize the skewness of the distribution in Question 1—positively skewed, negatively skewed, or approximately normal? Provide a rationale for your answer. The distribution in question 1 is skewed positively, when a skewed is positive it has the most statistic and it’s also more to the right side and the data is mostly on the right side, most people that participate in this study were mainly older generation. If it was a negative skewed it would be pointed more to the left meaning younger people participated.

Compare the original skewness statistic and Shapiro-Wilk statistic with those of the smaller dataset (n = 15) for the variable “Age at First Arrest.” How did the statistics change, and how would you explain these differences? When the original skewness statistic and Shapiro-Wilk is being compared, the original study n=20 and the n=15 has less skewness statistic. The graph of the n=15 shows a natural distribution than the original one. The new data value also is lower, the Shapiro-Wilk new statistic shows a p value of 0.211 and the new data statistic is within normal range where p is greater than 0.05.

 Age at Enrollment Frequency Percent Valid Percent Cumulative Percent Valid 41 1 6.7 6.7 6.7 43 1 6.7 6.7 13.3 47 1 6.7 6.7 20.0 49 1 6.7 6.7 26.7 52 2 13.3 13.3 40.0 56 3 20.0 20.0 60.0 58 1 6.7 6.7 66.7 60 2 13.3 13.3 80.0 62 1 6.7 6.7 86.7 63 2 13.3 13.3 100.0 Total 15 100.0 100.0

The distribution in question 1 is skewed positively, when a skewed is positive it has the most statistic and it’s also more to the right side and the data is mostly on the right side, most people that participate in this study were mainly older generation. If it was a negative skewed it would be pointed more to the left meaning younger people participated.

 Age at 1st Arrest Frequency Percent Valid Percent Cumulative Percent Valid 12 1 6.7 6.7 6.7 14 1 6.7 6.7 13.3 16 1 6.7 6.7 20.0 17 1 6.7 6.7 26.7 19 1 6.7 6.7 33.3 20 1 6.7 6.7 40.0 23 1 6.7 6.7 46.7 27 1 6.7 6.7 53.3 28 1 6.7 6.7 60.0 29 1 6.7 6.7 66.7 31 1 6.7 6.7 73.3 38 1 6.7 6.7 80.0 42 1 6.7 6.7 86.7 43 1 6.7 6.7 93.3 59 1 6.7 6.7 100.0 Total 15 100.0 100.0

 Descriptives Statistic Std. Error Age at Enrollment Mean 54.53 1.818 95% Confidence Interval for Mean Lower Bound 50.64 Upper Bound 58.43 5% Trimmed Mean 54.81 Median 56.00 Variance 49.552 Std. Deviation 7.039 Minimum 41 Maximum 63 Range 22 Interquartile Range 11 Skewness -.622 .580 Kurtosis -.600 1.121 Age at 1st Arrest Mean 27.87 3.366 95% Confidence Interval for Mean Lower Bound 20.65 Upper Bound 35.09 5% Trimmed Mean 27.02 Median 27.00 Variance 169.981 Std. Deviation 13.038 Minimum 12 Maximum 59 Range 47 Interquartile Range 21 Skewness .990 .580 Kurtosis .746 1.121

 Tests of Normality Kolmogorov-Smirnova Shapiro-Wilk Statistic df Sig. Statistic df Sig. Age at Enrollment .183 15 .192 .927 15 .248 Age at 1st Arrest .138 15 .200* .923 15 .211 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction

When the original skewness statistic and Shapiro-Wilk is being compared, the original study n=20 and the n=15 has less skewness statistic. The graph of the n=15 shows a natural distribution than the original one. The new data value also is lower, the Shapiro-Wilk new statistic shows a p value of 0.211 and the new data statistic is within normal range where p-value is greater than 0.05.

Q4. The way I would describe the Kurtosis of the question 4 distribution is leptokurtic, which is where the distribution is bunched around the mean which results higher

 Statistics Age at Enrollment N Valid 15 Missing 0 Skewness -.622 Std. Error of Skewness .580

The Skewness statistic can be reviewed in the data below it is 0.622. a skewness that is negative means most of statistic tail is on the left, which can be seen in the data below. The table shows that the data is a little bit skewed because the value between -1 and -1/2 or 1 and ½ is moderate.

 Statistics Years of Education N Valid 15 Missing 0 Skewness .658 Std. Error of Skewness .580 Kurtosis -.936 Std. Error of Kurtosis 1.121

The kurtosis for years of education is 0.936, when a value is negative for a kurtosis it means the tail of the statistic is light, and the data is mainly around the mean. Meaning the magnitude is less than one, meaning the value of kurtosis is moderate.

 Tests of Normality Kolmogorov-Smirnova Shapiro-Wilk Statistic df Sig. Statistic df Sig. Number of Times Fired from Job .311 15 .000 .737 15 .001 a. Lilliefors Significance Correction

Using the SPSS with the Shapiro-Wilk it’s a test that diverge from a normal distribution, meaning if a p value is less than 0.05 it can be used to verify if a distribution is normal or not. In this example the value 0.001 meaning the number is not standard from the amount of times getting tired from a job.

The Kolmogorov-Smirnov is inappropriate to report because its usually used for larger sample sizes, normally it’s not being used until the samples sizes got to 2,000.

It’s not very uncommon for the skewness to be low and the Shapiro-Wilk to be high. Skewness measures the moves over of the tail of the graph from the mean, if its low the tails becomes equal and they move over from the mean. On the other hand the Shapiro-Wilk look at the whole shape of the distribution all together, meaning the data may be non-parametric, or doesn’t follow any distribution at all.

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