# Goodness of fit

### Goodness of fit

This is a term that implies how well the sample data fits a distribution. In simple terms, it is used to check whether the data at hand is from the same distribution.  It establishes the difference between the data that you are trying to test and the data from the true population. It should be noted that before conducting any statistical tests such as ANOVA, there are certain assumptions about the distribution of the data that must be upheld before we could think of the analysis. For ANOVA, the data must be normally distributed. How can we know if the data is normally distributed?  For example, when the test is trying to establish the goodness of fit of the data sets.

Different types of the goodness of fit measures

In general, the goodness of fit measures can be categorized into two-the ones which conduct hypothesis testing and the ones that test whether the outcome of the frequencies tests the distribution.  For the ones that employ the hypothesis testing, the p-value is used to determine if the test is normally distributed.  Hypothesis testing methods include the Shapiro-Wilk test and the Kolmogorov-Smirnov test, while the common example for the other category is the chi-square test.

Shapiro-Wilk test

Well, it might come to you as a surprise that it is a test of goodness of fit. Most of the people identify it as a test of normality.  Here, we try to establish if the data fits a normal distribution.  Normality is a requirement in most of the statistical modeling data. The null hypothesis for the Shapiro-Wilk test in SPSS is that the data is normally distributed. The Shapiro-Wilk test is preferred for smaller datasets.

Kolmogorov-Smirnov test

It’s more like that Shapiro-Wilk test. The test is more appropriate for large datasets exceeding over 2000 rows.  The main advantage of the test is that it does not give you any assumptions about the dataset.

The chi-square

The chi-square goodness of fit test should not be confused with the chi-square independence test. There is a difference between the two tests. The chi-square goodness of fit is the one that fits a categorical variable to a distribution. The other test of independence compares two data sets to see if a relationship exists between the two.

The goodness of fit chi-square test is appropriate for fitting data to discrete distributions such as binomial and Poisson. The main disadvantage of the chi-square test is that it requires enough sample size to test for goodness of fit of a dataset.

Use the chi-square test when the sampling method obtained to collect the data is simple random sampling, and when you are studying categorical variables.

The null hypothesis for the chi-square test should, therefore, be used when the data is consistent with the distribution that you are using.

### Linear regression goodness of fit

The adjusted r-squared is a statistical term that is used to show the goodness of fit of a multiple regression model. It’s used where there are many variables. The adjusted r-squared value is a value that ranges from zero to one. When performing linear regression, you would prefer a value that is approaching one as it implies that the data is a perfect fit for your model. A smaller value is a strong indication that you should look for another data set for analysis or try out a new model. The adjusted r-squared is not a test that is conducted on a dataset. The result comes with the linear regression result table.

### The goodness of fit with SPSS

SPSS is a statistical software that is easy to learn. Most people who use it prefer it because of its user friendliness, it will not take you days to master how to use SPSS.  You would like it for the fact that you can perform complex statistical analyses without coding.

### The goodness of fit assignment help

The goodness of fit analysis is one of the things that a data analyst must do before fitting the model. It contributes to getting results that are more accurate from the analysis process. Therefore, expect lots of assignments in this area if you are studying statistics.

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