I would like to make the process of understanding hypothesis testing much simpler for students need help learning statistics. Hypothesis testing is a five-step procedure. Let’s address the difficulties of students while they learn the topic of hypothesis testing.
Step 1: Identifying the claim and designing null and alternative hypothesis
Students should first identify the research claim: A research claim is a statement or condition that is being tested.
Now if the claim is to test that there is NO difference between or to test if the given value is EQUAL to any number, in this case, we consider the claim as a null hypothesis.
In contrast, if the claim is to test that there is a difference or to test if the given number is NOT equal to/greater than/less than any given number, in this case, we consider the claim as an alternative hypothesis.
We represent the Null hypothesis symbolically with H0 and the alternative hypothesis with Ha or H1
Step 2: Identifying the tail of the test and notifying the significance level if given
Here, students are posed with the question: how do I identify the tail of the f test?
- It is simple if the alternative hypothesis is directional with the statement (greater than or less than) then the claim is ONE tailed.
- If the claim is with the statement NOT equal to-it is TWO tailed.
So when the claim is directional, it is a one-tailed test and when the claim is non-directional, it is a two-tailed test!
Step 3: Identifying the type of statistical test to be identified and to compute test statistic
Well there are different test statistics we compute while working with test statistics.
To start off, if we are testing one sample mean when the sample size is small (less than 30) and the standard deviation is unknown, we compute test statistic t for the same condition. When the standard deviation is known, we compute test statistic Z. We have different formulas listed for computing the Z test for one sample proportion and the difference between means and then the difference between proportions, so here to compute the test statistic we must identify the type of statistical test to be performed.
Step 4: Writing decisions
This is again a very confusing part to most of the students. There are two methods to write decisions, so students should be familiar with the method taught in class.
The first method is: P-Value Approach
In the p-value approach, we compare the p-value of the test statistic with the alpha/significance level.
- When the p-value is <(less than) Alpha we reject H0
- When the p-value is >(greater than) Alpha we fail to reject H0
The second method is: Critical Value Approach
So in this method, we compare test statistics obtained with the critical value of the test conducted
- When the test statistic is less than (<) critical value of the test we fail to reject H0
- When the test statistic is greater than(>) critical value of the test we reject H0
Step 5: Drawing conclusions
Students should match the decision results while making conclusions when we reject the null hypothesis we conclude that we have enough evidence.
To support the claim (in this case the claim will be an alternative hypothesis), we say the test is statistically significant.
When we reject the null hypothesis and say that we do not have enough evidence to support the claim (in this case the null hypothesis is the claim), we say the test is not statistically significant.
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