Statistics for everyone: ch.3 Nomality test and Variances test

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ch.3 Nomality test and Variances test

Testing whether a distribution is a normal distribution is called a normality test. This is not to examine whether the current sample is a normal distribution, but to see the population from which the current sample population came, is a normal group or not. In other words, we try to deduce if the mother population( or whole population or whole original population) shows a normal distribution.

Select the two variables as shown above, and then choose the one you want from the 6 normality blacks (red squares). I chose the commonly used ‘Shapiro-Wilk’.

Since there are 2 populations, the ‘Shapiro-Wilk normality test’ has been performed 2 times, and OJ rejects the null hypothesis that it has a normal distribution because it is p<0.05. In other words, we conclude that ‘the population of OJs does not come from a normal distribution.’

Observing whether the variance of different groups is the same is called an ‘homogeneity of variance test’. This, too, is not about each sample group, but about examining whether the original populations have equal variance. Let’s choose one of the 3 methods. Levene’s Test and Bartlett’s Test are commonly used. Levene’s test and Bartlett’s tests are available in two groups and more, and the F test is only available in two groups.

Again, select both variables in the same way as before.

Levene’s test has 2 methods, depending on mean and median.

A p<0.05 rejects the null hypothesis. The null hypothesis in this case is ‘equal variance’, so if you reject it, you are judging that ‘the variance of populations is not eaual’.

On the other hand, p>0.05 does not mean adopting the null hypothesis. It’s easy to think so, but it’s more true that ‘you can’t judge’. It may seem too complicated, and some people simply explain that they are simply and roughly adopting the null hypothesis, (p>0.05 is judged as equal variance).

Now let’s look at plots that look at normality and variance.

The most common and easiest thing to make to see the distribution is the histogram.

Specify both variables in the same way.

OJ shows an asymmetric distribution.

densitograms are used a lot in conjunction with histograms.

Select both variables in the same way.

Representing the distribution in curves, VC shows almost bell-shape symmetry.

QQ plot is designed specifically for normaly tests.

Set the variables to be the same. If the circle points are on a straight line, we determine that they have a normal distribution. Dotted lines also act as boundaries.

The two figures above can be used to determine normality or isovariance. It also shows the distribution itself, so it can also be used in papers and publications on its own.

The QQ plot is great for viewing isovariance, especially when looking at a small population of samples. It is not usually used for papers or presentations, but is often used in the middle of analyzing research results.

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