Other's On-Line Resources (Chapter 7)

 

Hypotheses
  • Description:
    Through clearly-written text and wonderful graphics, this on-line reource (1) clarifies the difference between null and alternative hypotheses, and (2) shows how different versions of the alternative hypothesis lead either to a one-tailed test or to a two-tailed test.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Hypotheses."
    2. Carefully read the text material and examine the various pictures.
    3. Click on the term "inductive research" if you'd like to get a brief explanation of how this form of scientific thinking works.

  • Sky Huck's Puzzle Questions:
    (1) It is stated in this on-line resource that of the two hypotheses being discussed (null and alternative), one of them describes the researcher's prediction. Why is this sometimes not true? (2) Near the end of this on-line resource, you're told what to do if your original prediction is not supported by the data. Do you agree?
     
Type I Errors
  • Description:
    By using this interactive on-line resource, you'll come to understand fully what it means to "commit" a Type I Error. Moreover, you'll be able to see this kind of error take place right before your eyes.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Type I Errors."
    2. After clicking on "Begin," change (in the next screen) the mean for Population B from 15 to 10. This makes the two population means identical. In other words, the null hypothesis (Ho: mA = mB) is true as we now check to see if the mean of a sample drawn from Population A is significantly different from the mean of a sample drawn from Population B.
    3. Click "Simulate" and look inside the gray box to see if the t-test's calculated value (disregarding its sign) is equal to or larger than the critical value. If so, we reject the null hypothesis. This decision is summarized in the upper right-hand portion of the screen where a "1" will appear next to "Significant" or "Not significant."
    4. Click on the "Simulate" button about 20 times while watching what happens in terms of the frequency counts that appear next to "Significant" and "Not significant." Whenever the number in the "Significant" window goes up, this is because a Type I Error has been made.
    5. Now click on "Simulate 5000" and look to see what appears in the "Percent Significant" window. This number should approximate .05, the level of significance.

  • Sky Huck's Puzzle Question:
    Click the "Reset" button, change the mean for Population B from 15 to 10, and then change the n from 8 to 100. What effect, if any, do you think this change in the sample size will have on the occurrence of Type I Errors? After making your guess, click on "Simulate 5000" to see what happens.
     
Type II Errors
  • Description:
    By using this interactive on-line resource, you'll come to understand fully what it means to "commit" a Type II Error. Moreover, you'll be able to see this kind of error take place right before your eyes.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Type II Errors."
    2. After clicking on "Begin," note (in the next screen) that the mean for Population A is 10 whereas the mean for Population B is 15. Clearly, two population means are different. In other words, if we now conduct a study to see if the mean of a sample drawn from Population A is significantly different from the mean of a sample drawn from Population B, the null hypothesis (Ho: mA = mB) is false.
    3. Click "Simulate" and look inside the gray box to see if the t-test's calculated value (disregarding its sign) is equal to or larger than the critical value. If so, we reject the null hypothesis; if not, we fail-to-reject the null hypothesis. This decision is summarized in the upper right-hand portion of the screen where a "1" will appear next to "Significant" or "Not significant."
    4. Click on the "Simulate" button about 20 times while watching what happens in terms of the frequency counts that appear next to "Significant" and "Not significant." Whenever the number in the "Not significant" window goes up, this is because a Type II Error has been made.
    5. Now click on "Simulate 5000" and look to see what appears in the "Percent Significant" window. This number will turn out to be quite a bit lower that 100%, thus suggesting that this particular t-test comparison has about a 30% chance of leading to a Type II Error.

  • Sky Huck's Puzzle Question:
    Click the "Reset" button and then change the n from 8 to 100. What effect, if any, do you think this change in the sample size will have on the occurrence of Type II Errors? After making your guess, click on "Simulate 5000" to see what happens.
     

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Schuyler W. Huck
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