Chi-Square test for Qualitative Data



WHEN SHOULD YOU USE THE Z TEST?

Qualitative data

Comparing PROPORTIONS of TWO groups

Sample data

You want to analyze the results of a famous health-study experiment that investigated the effectiveness of aspirin in the reduction of the incidence of heart attacks. In this experiment, 22.071 male U.S. physicians were randomly assigned to either a group that was given one 325 mg buffered aspirin tablet every other day or a group that was given a placebo. The results of the 5-year study follow:

Step 1: Make a two-way cross-classification table for the results.

Incidence of Heart Attacks in Physicians Taking Aspirin or Placebo

| |Study Group |

| |Aspirin |Placebo |Total |

|Results |Heart attack |104 |189 |293 |

| |No heart attack |10 933 |10 845 |21 778 |

|Total |11 037 |11 034 |22 071 |

Step 2: State the null hypothesis.

There is no significant difference in the proportions of heart attacks between the group that was given aspirin and the group that was given the placebo.

Step 3: Establish the level of significance (0.05).

Step 4: Calculate Z using the graphing calculator or Excel (see Lewis or Root).

|Z Test for the Difference in Two Proportions |

| | |

|Data |

|Hypothesized Difference |0 |

|Level of Significance |0.05 |

|Group 1 |  |

|Number of Successes |104 |

|Sample Size |11037 |

|Group 2 |  |

|Number of Successes |189 |

|Sample Size |11034 |

| | |

|Intermediate Calculations |

|Group 1 Proportion |0.0094 |

|Group 2 Proportion |0.0171 |

|Difference in Two Proportions |-0.0077 |

|Average Proportion |0.0133 |

|Z Test Statistic |-5.0014 |

|  |  |

|Two-Tail Test |  |

|Lower Critical Value |-1.9600 |

|Upper Critical Value |1.9600 |

|p-Value |0.0000 |

|Reject the null hypothesis |  |

Results from TI-84:

2 – PropZTest

p1 < p2

z = - 5.001388204

p = 2.8504563E -7 (p value)

p1 = .0094228504 (Group 1 proportion)

p2 = .0171288744 (Group 2 proportion)

p = .0132753387 (Average proportion)

n1 = 11037

n2 = 11034

Results from Excel

Step 5: Compare the calculated value for Z to the critical value of Z.

Lower critical value for Z is -1.96.

Upper critical value for Z is 1.96.

Step 6: Decide to reject or not reject the null hypothesis.

Calculated Z < -1.96 → null hypothesis is rejected

Calculated Z > 1.96 → null hypothesis is rejected

Calculated Z = -1.96 to 1.96 → null hypothesis is not rejected

Critical Z at 0.05 level.= ± 1.96; calculated Z of -5.00 < -1.96

The null hypothesis is rejected.

Step 7: Determine whether the statistical findings support the research hypothesis.

IF Null hypothesis was rejected = research hypothesis was supported

IF Null hypothesis not rejected = research hypothesis was not supported

Because the null hypothesis was rejected, the research hypothesis that physicians taking aspirin would have fewer heart attacks than physicians taking a placebo is supported.

Step 8: Construct a data table that communicates all statistics.

Table A: Incidence of Heart Attacks in Physicians Taking Aspirin or Placebo

| |Study Group |

| |Aspirin |Placebo |Total |

|Results |Heart attack |104 |189 |293 |

| |No heart attack |10 933 |10 845 |21 778 |

|Total |11 037 |11 034 |22 071 |

| | | |Average |

|Proportions |0.0094 |0.0171 |0.0133 |

|Z = -5.00 |Z of -5.00 < -1.96 p = 0.00 |

|Critical Z = ±1.96 | |

Step 9: Write a paragraph describing the results.

□ Write a topic sentence stating the independent and dependent variables, and a reference to

tables and graphs.

The proportions of heart attacks in physicians taking aspirin or placebo for a five-year study are summarized in Table A and Graph A.

□ Write sentences comparing the proportions of the groups.

Physicians taking aspirin during the five-year study had a lower proportion of heart attacks (.0094) compared to physicians taking a placebo (.0171)

□ Write sentences describing the statistical test, level of significance, and null hypothesis.

The Z test (p1< p2) was used to test the following null hypothesis at the 0.05 level of significance:

There is no significant difference in the proportions of heart attacks between the group that was given aspirin and the group that was given the placebo..

□ Write sentences comparing the calculated Z value with the critical Z value and make a

statement about rejection of the null hypothesis.

The null hypothesis was rejected (Z = -5.00 < -1.96; p =0.00)

□ Write sentences stating support of the research hypothesis by the data.

The data did support the research hypothesis that physicians taking aspirin would have fewer heart attacks than physicians taking a placebo.

Step 10: Construct a bar graph to illustrate the proportions for each group.

Proportion of Heart Attack Incidents for Physicians Taking Aspirin or Placebo

[pic]

Step 11: Write an appropriate conclusion.

• What was the purpose of the experiment?

The effectiveness of aspirin in the reduction of the incidence of heart attack was investigated by randomly assigning physicians to two groups. One group took aspirin every other day and the other group took a placebo every other day. The study was continued for five years.

• What were the major findings? (Focus on results of the statistical test)

There was a significant difference among the proportions of heart attacks between the two groups.

• Was the research hypothesis supported by the data?

The research hypothesis that physicians taking aspirin would have fewer heart attacks than physicians taking a placebo was supported. The Z test for p1 < p2 was calculated and the null hypothesis was rejected.

• How did your findings compare (similarities and differences) with your preliminary research?

Similarly, a ten-year study in England found that taking aspirin was effective in preventing heart attacks (Jarvak 246).

• What possible explanations can you offer for similarities and/or differences between your results and other researchers?

Both studies randomly assigned groups to the aspirin and placebo and continued for an extended period of time. The studies both involved a large number of individuals. The Jarvak experiment was more inclusive; this research had only physicians participating. It is possible that physicians have a healthier lifestyle, contributing to fewer heart attacks.

• What recommendations do you have for further study and for improving the experiment?

Additional investigations should be conducted to determine if the aspirin was the variable that decreased the number of heart attacks. Better experimental design will limit the other variables that may contribute to heart attack.

NOTE: You should be able to write much more than I did. After all, you did an extensive literature review before experimentation and you are the “expert” for your topic.

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