Question

Define the three types of hypothesis tests and explain why they are used. Give an example for each.

Answer 1

Hypothesis testing:

=>The hypothesis testing refers to the predefined formal procedures that are used by statisticians whether to accept or reject the hypotheses.

=>Hypothesis testing is defined as the process of choosing hypotheses for a particular probability distribution, on the basis of observed data

There are a number of different types of hypothesis tests

1.

T-test: tests for a Student’s t-distribution – ie, in a normally distributed population where standard deviation in unknown and sample size is comparatively small. Paired t-tests compare two samples.

example;

=>

Let’s say you have a cold and you try a naturopathic remedy. Your cold lasts a couple of days.

=>The next time you have a cold, you buy an over-the-counter pharmaceutical and the cold lasts a week. You survey your friends and they all tell you that their colds were of a shorter duration (an average of 3 days) when they took the homeopathic remedy.

=>What you really want to know is, are these results repeatable? A t test can tell you by comparing the means of the two groups and letting you know the probability of those results happening by chance.

2.Chi-Square Test for Independence: tests for an association of significance between two categorical variables in a population sample. Typically used with random sampling.

example

a scientist wants to know if education level and marital status are related for all people in some country. He collects data on a simple random sample of n = 300 people, part of which are shown below.

3. Analysis of Variance (ANOVA): tests for and analyzes differences between the means in several groups. Often used similarly to a t-test, but for more than two groups.

example:

=>you might want to find out if there is an interaction between income and gender for anxiety level at job interviews.

=>The anxiety level is the outcome, or the variable that can be measured. Gender and Income are the two categorical variables.

=>These categorical variables are also the independent variables, which are called factors in a Two Way ANOVA.