Steps in Hypothesis Testing

Prerequisites Introduction to Hypothesis Testing, Statistical Significance, Type I and II Errors

Questions

• What is the difference between a significance level and a probability level?
• What are the four steps involved in significance testing?

Step 1: State the Null Hypothesis

For a two tailed test, the null hypothesis is typically that a parameter equals zero although there are exceptions

• A typical null hypothesis is μ1 - μ2 = 0 which is equivalent to μ1 = μ2

For a one-tailed test, the null hypothesis is either that a parameter is:

• greater than or equal to zero
• less than
• equal to zero

If the prediction is that μ1 > μ2, then the null hypothesis (the reverse of the prediction) is μ1 ≤ μ2

Step 2: Specify the α level (significance level)

• Typical values are 0.05 and 0.01

Step 3: Compute the P-value

• This is the probability of obtaining a sample statistic as different or more different from the parameter specified in the null hypothesis given that the null hypothesis is true

Step 4: Compare the probability value with the α level

• If the probability value is lower then you reject the null hypothesis
• Keep in mind that rejecting the null hypothesis is not an all-or-none decision
• The lower the probability value, the more confidence you can have that the null hypothesis is false
• However, if your probability value is higher than the conventional α level of 0.05, most scientists will consider your findings inconclusive
• Failure to reject the null hypothesis does not constitute support for the null hypothesis
• It just means you do not have sufficiently strong data to reject it

Questions

1 First you decide on the null hypothesis. Then you analyze the data and calculate the probability value. You look at this probability value, and depending on what it is, you then choose an appropriate alpha level. Then you decide whether you can reject the null hypothesis.

	True
	False

Answer >>

You want to select the alpha level before you calculate the probability value. You compare your probability value to your previously selected alpha level when deciding whether you can reject the null hypothesis.

2 The goal of research is to prove that the null hypothesis is true.

	True
	False

Answer >>

Researchers generally specify a null hypothesis that is the opposite of what they are predicting. Getting a p value lower than the alpha level allows you to reject the null hypothesis, but getting a p value greater than the alpha level does not prove that the null hypothesis is true.