What is the significance of f test

Figure 5: X2 residuals plot. Figure 6: Setting up the data in the table of an online calculator. Figure 7: Regression statistics. Table 5: Correlation matrix Click here to view. Figure 8: Residual plots.

Interpretation of the Output. Table 8: Data on use of hypotensive drugs Click here to view. Figure 9: Residual plots. Table 9: Correlation matrix Click here to view. Figure Regression statistics. This article has been cited by. Estimation of daily diffuse solar radiation from clearness index, sunshine duration and meteorological parameters for different climatic conditions.

Sustainable Energy Technologies and Assessments. Related articles F-test hypothesis testing online calculator regression. Access Statistics. Assumptions Unde Years ago, statisticians discovered that when pairs of samples are taken from a normal population, the ratios of the variances of the samples in each pair will always follow the same distribution.

Not surprisingly, over the intervening years, statisticians have found that the ratio of sample variances collected in a number of different ways follow this same distribution, the F-distribution. Because we know that sampling distributions of the ratio of variances follow a known distribution, we can conduct hypothesis tests using the ratio of variances.

Remember that the sample variance is:. Think about the shape that the F-distribution will have. If s 1 2 and s 2 2 come from samples from the same population, then if many pairs of samples were taken and F-scores computed, most of those F-scores would be close to one. All of the F-scores will be positive since variances are always positive — the numerator in the formula is the sum of squares, so it will be positive, the denominator is the sample size minus one, which will also be positive.

Thinking about ratios requires some care. If s 1 2 is a lot larger than s 2 2 , F can be quite large. It is equally possible for s 2 2 to be a lot larger than s 1 2 , and then F would be very close to zero. Since F goes from zero to very large, with most of the values around one, it is obviously not symmetric; there is a long tail to the right, and a steep descent to zero on the left.

There are two uses of the F-distribution that will be discussed in this chapter. The first is a very simple test to see if two samples come from populations with the same variance. The second is one-way analysis of variance ANOVA , which uses the F-distribution to test to see if three or more samples come from populations with the same mean. Because the F-distribution is generated by drawing two samples from the same normal population, it can be used to test the hypothesis that two samples come from populations with the same variance.

You would have two samples one of size n 1 and one of size n 2 and the sample variance from each. Obviously, if the two variances are very close to being equal the two samples could easily have come from populations with equal variances. Because the F-statistic is the ratio of two sample variances, when the two sample variances are close to equal, the F-score is close to one. If you compute the F-score, and it is close to one, you accept your hypothesis that the samples come from populations with the same variance.

This is the basic method of the F-test. Hypothesize that the samples come from populations with the same variance. Compute the F-score by finding the ratio of the sample variances. If the F-score is close to one, conclude that your hypothesis is correct and that the samples do come from populations with equal variances. If the F-score is far from one, then conclude that the populations probably have different variances.

The basic method must be fleshed out with some details if you are going to use this test at work. There are two sets of details: first, formally writing hypotheses, and second, using the F-distribution tables so that you can tell if your F-score is close to one or not.

Formally, two hypotheses are needed for completeness. The first is the null hypothesis that there is no difference hence null. It is usually denoted as H o. It is used when the sample size is small i. For example, suppose one is interested to test if there is any significant difference between the mean height of male and female students in a particular college.

In such a situation, a t-test for difference of means can be used. However one assumption of the t-test is that the variance of the two populations is equal; in this case the two populations are the populations of heights for male and female students.

Unless this assumption is true, the t-test for difference of means cannot be carried out. The F-test can be used to test the hypothesis that the population variances are equal. There are different types of t-tests for different purposes. Some of the more common types are outlined below. F-test for testing equality of variance is used to test the hypothesis of the equality of two population variances. The height example above requires the use of this test.

F-test for testing equality of several means. For example, suppose that an experimenter wishes to test the efficacy of a drug at three levels: mg, mg and mg. A test is conducted among fifteen human subjects taken at random, with five subjects being administered each level of the drug. If your entire model is statistically significant, that's great news!

However, be sure to check the residual plots so you can trust the results! If you're learning about regression, read my regression tutorial! Minitab Blog. Minitab Blog Editor 11 June, The hypotheses for the F-test of the overall significance are as follows: Null hypothesis : The fit of the intercept-only model and your model are equal.

Alternative hypothesis : The fit of the intercept-only model is significantly reduced compared to your model. That set of terms you included in your model improved the fit!