Other's On-Line Resources (Chapter 17)

 

2x3 Chi Square
  • Description:
    This interactive on-line resource gives you the chance to (a) change the cell frequencies in a 2x3 contingency table and then (b) see what the chi-square calculated value and accompanying p-level are for your data.

  • What to Do:
    1. Click on the colored title of this on-line resource: "2x3 Chi Square."
    2. On the screen that pops up, scroll down (if you need to) until you see a rectangle containing 3 rows ("Male," "Female," and "Total") and 4 columns ("White," "Black," "Hispanic," and "Total").
    3. Click on each of the cells in the contingency table (but not on those in the "Total" row or column) and change the numbers.
    4. Click on the "Compute!" button, and then examine the numbers in the "Chi square" and "p-level" boxes.
    5. Repeat Steps 3 and 4 several times until you get a feel for the kinds of data sets that cause p to be large or small.

  • Sky Huck's Puzzle Question:
    It's possible to fill the 6 cells of the 2x3 contingency table with 6 different numbers and yet have p turn out equal to 1, thus indicating the the sample data are perfectly aligned with the null hypothesis. Can you do this?
     
Tests of Proportions
  • Description:
    In using this interactive on-line resource, you'll be able to simulate what happens when a one-sample test of a proportion is used. After exerting control over what the null hypothesis says and several other important things (such as the nature of the alternative hypothesis and the level of significance), you'll get to see a visual display of the results when 100 random samples are evaluated.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Tests of Proportions."
    2. Scroll down to the gray horizontal bar that is positioned above a wide pink rectangle.
    3. Click on the "Play" button that's located near the right end of the gray bar.
    4. Examine the information that's presented above, in, and below the pink bar so as to get a feel for what's going on.
    5. Each of the tests you just conducted was one-tailed in nature. Repeat the simulation, this time in a two-tailed fashion; to do this, choose the bottom option in the pull-down menu near the left end of the gray bar. Then, click the "Play" button.
    6. Make changes in (a) the null number in the "p0" box (so it's something other than .5), (b) the value of the population proportion in the "p" box (so it's something other than .5), and (c) the level of significance. After each change you make, click on the "Play" button to see what happens.

  • Sky Huck's Puzzle Question:
    What is the meaning of the exclamation point that appears in one of the "Ha" options in the gray bar?
     
Chi Square and Yates
  • Description:
    In using this interactive on-line resource, you'll be able to (1) see how the Yates correction makes the chi-square test more conservative and (2) investigate for yourself whether the Yates correction is too conservative.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Chi Square and Yates."
    2. After clicking on "Begin," you'll get a new screen that has 3 gray boxes. In the upper left-hand box, you'll see that the probability for success is 0.6 for both of the two hypothetical conditions being compared. With both probabilities the same, the null hypothesis is true.
    3. Click on "Simulate 1" to see, in the two gray boxes on the right, what happens when sample data are extracted from the hypothetical populations and analyzed by a chi-square test, both with and without the Yates correction.
    4. Now click on "Simulate 5000" to see, in the lower right-hand box, what would happen over 5,000 replications. Of course, with the significance level set at 0.05 (see upper right-hand box) and with the null hypothesis being true, 5% of the results should be significant.

  • Sky Huck's Puzzle Question:
    Change the 2 values of "N" in the upper left-hand box from 10 to 20. Now, with larger sample sizes, what do you think the "Proportion significant" number will be if you click "Simulate 5000"? Click and see. Then increase N again and repeat the simulation. What do you see happening?
     
Fisher's Exact Test
  • Description:
    In using this interactive on-line resource, you'll be able to enter data into a 2x2 contingency table and then see the p-level that's computed for your data. By entering various combinations of hypothetical data, you'll come to understand why a Fisher's Exact Test sometimes leads to a statistically significant result.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Fisher's Exact Test."
    2. On the screen that pops up, locate the 4 open boxes labeled "a," "b," "c," and "d."
    3. Imagine that boxes "a" and "b" represent the number of males who did and didn't get at least 1 traffic ticket during the past 6 months. Likewise, imagine that boxes "c" and "d" represent the number of females who did and didn't get at least 1 traffic ticket during the past 6 months.
    4. Enter the number 5 in each of the 4 boxes and then cliock "Please Calculate Now." Look at the p-level that's displayed on the next screen that pops up.
    5. Click on your browser's "back" button, repeat Step #4 with different numbers going into the 4 cells, and then repeat this process several times until you get a "feel" for what kinds of data sets cause Fisher's Exact Test to yield small p-levels.

  • Sky Huck's Puzzle Question:
    Suppose you were to begin with the number 2 in each of the 4 cells of the 2x2 contingency table. Further suppose that you now could do one of two things: (1) add 5 to cell "b" and add 5 to cell "c" OR (2) add 10 to cell "b." Which of these changes do you think would lead to the smaller p-level? After making your guess, make both changes, examine the 2 p-levels, and see if your guess was correct.
     

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Schuyler W. Huck
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