Statistic Assignment - Analysis and Interpretation
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This assignment provides an analysis and interpretation of statistical data related to age, education, and employment. The distribution, skewness, kurtosis, and normality of the data are discussed.
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Running head: STATISTIC ASSIGNMENT Statistic Assignment Name of Student Name of University Author Note
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3STATISTIC ASSIGNMENT Q2. 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. Q3. Age at 1st Arrest
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4STATISTIC ASSIGNMENT FrequencyPercentValid PercentCumulative Percent Valid 1216.76.76.7 1416.76.713.3 1616.76.720.0 1716.76.726.7 1916.76.733.3 2016.76.740.0 2316.76.746.7 2716.76.753.3 2816.76.760.0 2916.76.766.7 3116.76.773.3 3816.76.780.0 4216.76.786.7 4316.76.793.3 5916.76.7100.0 Total15100.0100.0 Descriptives StatisticStd. Error Age at Enrollment Mean54.531.818 95% Confidence Interval for Mean Lower Bound50.64 Upper Bound58.43 5% Trimmed Mean54.81 Median56.00 Variance49.552 Std. Deviation7.039 Minimum41 Maximum63 Range22 Interquartile Range11 Skewness-.622.580 Kurtosis-.6001.121 Age at 1st ArrestMean27.873.366 95% Confidence Interval for Mean Lower Bound20.65 Upper Bound35.09 5% Trimmed Mean27.02 Median27.00 Variance169.981
5STATISTIC ASSIGNMENT Std. Deviation13.038 Minimum12 Maximum59 Range47 Interquartile Range21 Skewness.990.580 Kurtosis.7461.121 Tests of Normality Kolmogorov-SmirnovaShapiro-Wilk StatisticdfSig.StatisticdfSig. Age at Enrollment.18315.192.92715.248 Age at 1st Arrest.13815.200*.92315.211 *. 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.
6STATISTIC ASSIGNMENT Q4. Q5. 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 Q6. Statistics Age at Enrollment NValid15 Missing0 Skewness-.622 Std. Error of Skewness.580
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7STATISTIC ASSIGNMENT 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. Q7. Thekurtosisforyears of education is 0.936, when a value is negative fora kurtosis it means the tail of the statistic is light, andthe data is mainly around the mean. Meaning the magnitude is less than one, meaning the value of kurtosis is moderate. Q8. Tests of Normality Kolmogorov-SmirnovaShapiro-Wilk StatisticdfSig.StatisticdfSig. Number of Times Fired from Job.31115.000.73715.001 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. Statistics Years of Education NValid15 Missing0 Skewness.658 Std. Error of Skewness.580 Kurtosis-.936 Std. Error of Kurtosis1.121
8STATISTIC ASSIGNMENT Q9. 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. Q10. 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.