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Normality Test for Paired Data

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Zaenal Fanani

Academic year: 2024

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Paired Test

1. Parametric

Normality test

The significance values for the PreTest and PostTest are 0.05 and 0.02 respectively, based on the findings of the normality test. Given that the PreTest's significance value is precisely at the 0.05 threshold, the PreTest data is just shy of being classified as statistically regularly distributed. However, the PostTest data does not match the normality assumption, and as a result, it is deemed statistically non-normally distributed, with a significance value of less than 0.05.

2. Non-Parametric

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The negative ranks between individual performance during the pretest and posttest are 0 for N, Mean rank, and Sum of ranks. This indicates that there is no decrease from the pretest scores to the posttest scores.

- There are 36 positive data points (N), meaning 36 individuals experienced an improvement in performance. The Mean Rank is 18.50, while the sum of positive ranks is 666.000.

- Ties refer to the instances where the pretest and posttest scores are the same. In the data above, the number of ties (N) is 0, indicating that there are no identical scores between the pretest and posttest.

Based on the data above, the Asymp. Sig (2 Tailed) value is 0.00. Since 0.00 is less than 0.05, it indicates that there is a significant difference between the average results of the PreTest and PostTest.

An independent samples t-test

1. Normality Test

The purpose of the data normality uji is to determine if the sample used has a normal

distribution or not. Data normalization is performed using the Kolmogorov-Smirnov method

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in the SPSS software. The following criteria can be used to determine the asymptotic significance of a hypothesis:

1. If the probability (Sig.) is greater than 0.05, then the distribution is normal.

2. If the significance (Sig.) is less than 0.05, the distribution is non-normal

Tests of Normality

X

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

Y Education .209 474 .000 .906 474 .000

Salary .208 474 .000 .771 474 .000

a. Lilliefors Significance Correction

It can be seen from the above table that the significance level for both groups is less than 0.05. proving that the data do not follow a normal distribution.

2.T Test

Mann WhitneyTest is used to determine whether there are any differences between the two non-paired samples. If the data that will be analyzed by mann-whitney whitney is not normally distributed, then

Method for calculating the mean deviation:

1. If the sig. (2-tailed) value is less than 0.05, then there is a significant difference between the values of group 1 and group 2.

2. If the sig. (2-tailed) > 0.05, then there is no significant difference between the results of group 1 and group 2.

Ranks

X N Mean Rank Sum of Ranks

Y Education 474 237.50 112575.00

Salary 474 711.50 337251.00

Total 948

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Test Statisticsa

Y

Mann-Whitney U .000

Wilcoxon W 112575.000

Z -26.789

Asymp. Sig. (2-tailed) .000 a. Grouping Variable: X

It is evident from the table that the significance value is less than 0.05, with a value of 0.000.

Thus, it may be said that there is a notable distinction between salary and education. This indicates that the observed disparities between the groups are statistically significant and not the result of chance, suggesting that differences in salary are probably related to variances in education levels.

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