Statistical Tests

"A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a surgery of suppositions. "

Michael J. Moroney

You must be able to calculate Pearson's correlation momentum coefficient. For Spearman's test is noted as rs
Remember that when I have the same value in my raw data I take the average of the ranks
Spearman's correlation shows the extent to which one variable increases or decreases as the other variable increases.

The null hypothesis is rejected if either the statistic is more than the critical value or the p-value is less than the significance level.
If the null hypothesis is rejected we say the result is significant
The hypothesis test for the population correlation coefficient rho (ρ) will have H0 :ρ=0. The p value can be obtain from GDC.
Chi squared test for independence can be performed to find out if two data sets are independent of each other or not.The GDC will produce a table of expected frequencies and a p-value . If any expected frequencies are less than 5 then adjacent rows or columns need to be merged.
In a Chi squared goodness-of-fit-test , the degrees of freedom are v=n-1
To obtain the number of degrees of freedom, take the number of cells minus one, and then subtract one for each of the parameters estimated

When testing for a population mean, use z-test if the population standard deviation is known and the t-test if not
When testing for the differences between two means use the pooled t-test.
When two groups are paired find the difference between each pair and test H0 : μ=0

A probability of a type I error is the probability of rejecting H0 when H0 is true. For the normal distribution this will be equal to the significance level, for a discrete distribution this will be the probability of the statistic falling in the critical region.
In order to find the probability of a type II error, first find the critical region under the null hypothesis.
The probability of a type II error is the probability of the statistic not being in the critical region. This is calculated using a value for the parameter chosen from the alternative hypothesis.

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