Hypothesis or Significance Testing

  1. Start with a research question: For example, Do Bubba's magic pills cause a weight loss in adults who take them the perscribed one month period?

  2. 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).

  3. 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 a hypothesis. Remember that Ho represents no effect.

For the example of Bubba's magic pills, we will assume that we have monthly weight loss data for a large population of adults. Some would gain weight and some lose, but the loss would average about zero.

  
Ho: m = 0, Ha: m <0 

p = the area of the lower tail

 Ho: m = 0, Ha: m ≠0

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 = 0, Ha: m >0

p = the area of the upper tail

 

 

  1. Find the area under the curve for the appropriate tail that corresponds to the p-values as show above.

  2. 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.

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

If Alpha is Given

a) Decide whether to reject or fail to reject the null hypothesis

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

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

Example 1) Ho rejected (assuming alpha = 5%): Since the p-value of 0.0?% is less than 0.05, The sample is statistically significant at the 5% level, therefore we have sufficient evident to reject the null hypothesis and accept the alternative hypothesis that Bubba's magic pills caused a weight loss in the adults who took them as percribed.

Example 2) Ho accepted: Since the p-value of 0.0?% is greater than 0.05, the sample is not statistically significant at the 5% level, 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 adults who took them as percribed.

If Alpha is Not Given

a) Skip this step

 

 

 

b) 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 adults who took them as percribed.

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 adults who took them as percribed.