## What is Normality Test?

A normality test is a statistical tool used to determine if a sample or population of data follows a normal distribution. The normal distribution is also known as the Gaussian distribution or the bell curve, and it is characterized by its symmetrical shape, where the majority of the data points are clustered around the mean, and the tails of the distribution extend to infinity.

Normality tests are important in statistics because many statistical methods rely on the assumption of normality, such as t-tests, ANOVA, and regression analysis. If the data is not normally distributed, the results of these tests may be misleading or invalid.

There are several methods for testing normality, including graphical methods such as histograms and Q-Q plots, as well as statistical tests such as the Shapiro-Wilk test, the Kolmogorov-Smirnov test, and the Anderson-Darling test.

In the Shapiro-Wilk test, the null hypothesis is that the data comes from a normal distribution, while the alternative hypothesis is that the data does not come from a normal distribution. The test statistic is calculated based on the sample data, and if the p-value associated with the test statistic is less than the chosen significance level (e.g., 0.05), the null hypothesis is rejected, and it is concluded that the data is not normally distributed.

It is important to note that normality tests are not always necessary or appropriate. In some cases, the sample size may be too small to draw reliable conclusions from the test, or the data may not be expected to follow a normal distribution due to the nature of the variables being measured. In these cases, alternative statistical methods may be used.

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## Topics Covered in SPSS Normality Test assignments

SPSS (Statistical Package for the Social Sciences) is a statistical analysis software widely used by researchers in social sciences to conduct various types of analyses. One of the most common analyses performed using SPSS is the normality test. In this assignment, you are likely to be asked to perform a normality test using SPSS and interpret the results.

The normality test is used to determine whether the distribution of a dataset is approximately normal (i.e., bell-shaped) or not. A normal distribution is a theoretical distribution where the mean, median, and mode are all equal and the data is symmetrical around the mean. Many statistical tests assume that the data are normally distributed, and violating this assumption can lead to incorrect results. Thus, it is essential to test for normality before performing any statistical tests.

There are several methods to test for normality in SPSS. The most commonly used are the Shapiro-Wilk test and the Kolmogorov-Smirnov test. The Shapiro-Wilk test is a parametric test that assesses whether the data follow a normal distribution. It calculates a test statistic, W, and compares it to a critical value. If W is less than the critical value, the null hypothesis (that the data are normally distributed) is accepted. If W is greater than the critical value, the null hypothesis is rejected, indicating that the data are not normally distributed.

The Kolmogorov-Smirnov test is a nonparametric test that compares the cumulative distribution function of the sample data to the cumulative distribution function of the normal distribution. It calculates a test statistic, D, and compares it to a critical value. If D is less than the critical value, the null hypothesis (that the data are normally distributed) is accepted. If D is greater than the critical value, the null hypothesis is rejected, indicating that the data are not normally distributed.

In your assignment, you may also be asked to examine the normality of a dataset visually. This can be done by creating a histogram or a boxplot of the data. A histogram is a graphical representation of the frequency distribution of a dataset, while a boxplot shows the distribution of the data in terms of median, quartiles, and outliers.

Interpreting the results of a normality test is crucial in determining the appropriate statistical analysis to use. If the data are normally distributed, parametric tests such as t-tests and ANOVA can be used. If the data are not normally distributed, nonparametric tests such as the Mann-Whitney U test and the Kruskal-Wallis test should be used instead.

In summary, a normality test is a fundamental analysis used in social science research to test whether a dataset is normally distributed or not. It is important to understand the methods of testing for normality in SPSS, how to interpret the results, and how to use the results to determine the appropriate statistical analysis to use.

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## SPSS Normality Test assignment explanation with Examples

SPSS Normality Test is used to determine whether a data set follows a normal distribution or not. The normal distribution is a common statistical distribution that is symmetrical around the mean, and it is often used in statistical analyses because many statistical tests require data to be normally distributed. If the data is not normally distributed, some statistical tests may not be appropriate to use.

There are several tests available in SPSS to determine whether data is normally distributed or not. Some of the commonly used tests are:

Shapiro-Wilk test: This test is used to test the null hypothesis that the data is normally distributed. If the p-value is less than the significance level (usually 0.05), then the null hypothesis is rejected, and the data is not normally distributed.

Kolmogorov-Smirnov test: This test is used to compare the distribution of the data to a normal distribution. If the p-value is less than the significance level, then the null hypothesis is rejected, and the data is not normally distributed.

Anderson-Darling test: This test is similar to the Shapiro-Wilk test but is more sensitive to deviations from normality in the tails of the distribution.

Example: Suppose we want to determine whether the weights of a sample of 50 people are normally distributed.

Select “Analyse” from the menu, and then select “Descriptive Statistics,” followed by “Explore.”

Select the variable containing the weight data and move it into the “Dependent List” box.

Click the “Statistics” button and select “Normality Tests.” Choose the desired normality test (e.g., Shapiro-Wilk) and click “Continue.”

Click “OK” to run the analysis.

The output will include the test statistic, degrees of freedom, and p-value. If the p-value is greater than 0.05, then the data is normally distributed. If it is less than 0.05, then the data is not normally distributed.

It is important to note that a normality test does not prove that data is normally distributed, but rather it indicates whether there is evidence to reject the null hypothesis that the data is normally distributed. If the data is not normally distributed, there are alternative statistical tests that can be used.