8. Using SPSS, compute the Shapiro-Wilk statistic for “Number of Times Fired fro
ID: 3200306 • Letter: 8
Question
8. Using SPSS, compute the Shapiro-Wilk statistic for “Number of Times Fired from Job.” What would you conclude from the results?
9. In the SPSS output table titled “Tests of Normality,” the Shapiro-Wilk statistic is reported along with the Kolmogorov-Smirnov statistic. Why is the Kolmogorov-Smirnov statistic inappropriate to report for these example data?
10. How would you explain the skewness statistic for a particular frequency distribution being low and the Shapiro-Wilk statistic still being signi? cant at p < 0.05?
Most parametric statistics require that the variables being studied are normally distrib- uted. The normal curve has a symmetrical or equal distribution of scores around the mean with a small number of outliers in the two tails. The first step to determining normality is to create a frequency distribution of the variable (s being studied. A frequency distribu- tion can be displayed in a table or figure. A line graph figure can be created whereby the x axis consists of the possible values of that variable, and the y axis is the tally of each value. The frequency distributions presented in this Exercise focus on values of continu- ous variables. With a continuous variable, higher numbers represent more of that variable and the lower numbers represent less of that variable, or vice versa. Common examples of continuous variables are age, income, blood pressure, weight, height, pain levels, and health status (see Exercise 1) The frequency distribution of a variable can be presented in a frequency table, which is a way of organizing the data by listing every possible value in the first column of numbers, and the frequency (tally of each value as the second column of numbers. For example, consider the following hypothetical age data for patients from a primary care clinic. The ages of 20 patients were: 45, 26, 59, 51, 42, 28, 26, 32, 31, 55, 43, 47, 67, 39, 52, 48, 36, 42, 61, and 57 First, we must sort the patients' ages from lowest to highest values: 26 26 28 31 32 36 39 42 42 43 45 47 48 51 52 55 57 59 61 67Explanation / Answer
Answer:
8. Using SPSS, compute the Shapiro-Wilk statistic for “Number of Times Fired from Job.” What would you conclude from the results?
Tests of Normality
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
Number of times fired
.245
20
.003
.808
20
.001
a. Lilliefors Significance Correction
Assume the significance level at 0.05 than the p-value is smaller than alpha (0.001< 0.05) , we reject the null hypothesis and conclude that data not from the normal distribution.
9. In the SPSS output table titled “Tests of Normality,” the Shapiro-Wilk statistic is reported along with the Kolmogorov-Smirnov statistic. Why is the Kolmogorov-Smirnov statistic inappropriate to report for these example data?
The Shapiro-Wilk Test is more appropriate for small sample sizes (< 50 samples). Kolmogorov-Smirnov statistic is inappropriate or less power when sample size is small.
10. How would you explain the skewness statistic for a particular frequency distribution being low and the Shapiro-Wilk statistic still being signi cant at p < 0.05?
Shapiro-Wilk statistic examines the entire shape of the distribution while skewness and kurtosis statistics examine only skewness and kurtosis respectively. Therefore skewness statistic for a particular frequency distribution being low and the Shapiro-Wilk statistic still being signi cant at p < 0.05.
Descriptives
Statistic
Std. Error
Number of times fired
Mean
1.50
.407
95% Confidence Interval for Mean
Lower Bound
.65
Upper Bound
2.35
5% Trimmed Mean
1.33
Median
1.00
Variance
3.316
Std. Deviation
1.821
Minimum
0
Maximum
6
Range
6
Interquartile Range
3
Skewness
1.133
.512
Kurtosis
.576
.992
Tests of Normality
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
Number of times fired
.245
20
.003
.808
20
.001
a. Lilliefors Significance Correction
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