 # Goodness-of-fit

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I see a term in SPSS research about goodness of fit test. What does it mean by goodness of fit test? Is it a kind of hypothesis test? Please explain it.

### 1 comment to Goodness-of-fit

• Afroze

The goodness of fit is a statistical model which can explain how well set of observations are being fitted and it is a way to look at your frequency distributions fit in a specific pattern or no. For measuring this fitness his model can summarize the variance between the observe and expected values of a variable. This type of measurement can be use in Hypothesis testing, Analysis of variance and other tests in SPSS research. There is two values are involved, one is observed value which can get from sample and the other is expected which can calculated based upon the claimed distribution. The main idea in SPSS research is if the observed values are adjacent to the expected value then the square of deviations will be less. Here the term square division divided by expected value working as a weighted factor. If the sum of this weighted factor is small that means the observed values are close to the expected one. If this situation arises then researcher can establish a strong reason for not rejecting the hypothesis that variables are come form a same distribution. However, if the sum of weighted factor is large then there is no reason left to not rejecting the hypothesis, hence, the chi-square goodness-of-fit test is always gives you the right decision. Before doing this test research has to be aware of some conditions should be met. These are:

• The test statistic has a chi-square distribution
• Data are obtained from a random sample
• The expected values of each category should have at least 5 values/cases.
• The data should be normally distributed

Moreover, the likelihood ratio test can also be used for goodness of fit of a model. What’s more, if SPSS researcher wants to assess the given distribution is suited for the data set or not, he can use Kolmogorov–Smirnov/Cramér–von-Mises criterion/Anderson–Darling tests.