Hypothesis or Significance Testing

Start with a research question

1) Make a drawing of the sampling distribution for the null hypothesis and shade in the area representing the p-value. Remember, the mean on the drawing always matches with the m given in Ho (see below).

2)  State the null and alternative hypothesis mathematically one of three ways (note that Ho always has the same form). Always use a parameter never a statistic when stating the a hypothesis.

  
Ho: m = 12, Ha: m < 12 

p = the area of the lower tail

Ho: m = 12, Ha: m 12

p = the area of the both tails

Note: a two tailed test has a p-value twice as high as a single tailed test with the same data

 Ho: m = 12, Ha: m > 12

p = the area of the upper tail

 

3) Find the area under the curve using a statistic which corresponds to the p-value.

4) State the definition of p-value using the number you have just calculated.

Example for p-value = 3%:  The probability of obtaining a test statistic as extreme or more extreme than the one obtained is 3%, assuming Ho is true.

 

5) Write a conclusion that answers the original research question using the above statistical analysis.

If Alpha is Given

5) Decide whether to reject or fail to reject the null hypothesis based on comparing the p-value with alpha.

  • If: p-value alpha level   reject Ho
  • If: p-value > alpha level   fail to reject Ho

6) Write an English language sentence summarizing your findings. For example if the null is rejected you might write:

Example 1) Ho rejected: The sample is statistically significant at the alpha level  (p=?) therefore we reject the null hypothesis and accept the alternative hypothesis that Bubba's magic pills caused a weight loss in the subjects who took them.

Example 2) Ho accepted: The sample is not statistically significant at the alpha level  (p=?), therefore, we fail to reject the null hypothesis. There is not sufficient evidence to accept the alternative hypothesis that Bubba's magic pills caused a weight loss in the subjects who took them.

If Alpha is Not Given

5) Skip this step

 

6) Write an English language sentence summarizing your findings stating whether there is or is not strong statistical evidence for rejecting the null hypothesis. This is based on your judgment

Example 1) Ho rejected: The sample provides strong statistical evidence (p=?) for rejecting the null hypothesis hence, we accept the alternative hypothesis that Bubba's magic pills caused a weight loss in the subjects who took them.

Example 2) Ho accepted: The sample does not provide strong enough statistical evidence (p=?) for rejecting the null hypothesis, hence, we cannot accept the alternative hypothesis that Bubba's magic pills caused a weight loss in the subjects who took them.