Probability Rules

Weinberg and Abramowitz (2008) provide an example of simple probability concerning a set of students representing differing geographic regions.

Problem 1: If a student from the set is drawn at random with replacement, what is the probability that the student is from the Northeast?

Problem 2: If a second student is drawn at random with replacement, what is the probability that the student is from the South?

Problem 3: Using the additive rule [P(Ei or E2) = P(E1) + P(E2)], what is the probability that a student random drawn with replacement is from either the Northeast or the South?

Weinberg and Abramowitz (2008) explored computer usage of families with and eighth grader in these regions. The following crosstabulation gives us data:

Problem 1: What is the probability of selecting a student who is from the south or whose family owns a computer when the student was in the eighth grade? Using the probability rule [P(E ₁ or E ₂ ) = P(E ₁ ) + P(E2) - P(E ₁ land E ₂ )], calculate the probability.

Rosner: Table 8.17 Obstetrics (p. 311). The Independent-Samples t Test

A clinical trial is conducted to determine the effectiveness of drug A in preventing premature labor. Thirty women are randomly divided into a treatment group and a placebo group. Birth weights of infants born to the women are given below. Investigators wish to compare the birth weights of infants born to mothers within the treatment group with the infants born to mothers within the placebo group.

RQ: Is there a difference in the average birth weight in infants between those mothers who received drug A and those mothers who received the placebo?

Ho: mean birth weight treatment group = mean birth weight placebo group

Ha: mean birth weight treatment group does not equal mean birth weight placebo group

Step 1: Create the Variables

1. Start SPSS.
2. Click the Variable View tab.
3. Enter the variables therapy and weight in the rows.
4. Create value labels for therapy with 1 = drug A and 2 = placebo

The Data:

Step 2: Enter the data

1. Click Data View tab.
2. Enter the data for the 30 participants.

Step 3: Analyze the Data

1. From the menu bar, select Analyze>Compare Means> Independent-Samples T Test.
2. Select weight and move it into Test Variables box.
3. Select therapy and move in into Grouping Variable box, click Define Groups and enter a 1 beside drug A and a 2 beside placebo.
4. Click Continue.
5. Click OK.

Step 4: Interpret the Results

Effect Size =

Cohen (1988) specified values of d of .2, .5, and .8 as corresponding to small, medium, and large effect sizes.

Expression of Results in APA Format:

Daniel 7.2.12

The following data are oxygen uptakes (milliliters) during incubation of a random sample of 15 cell cultures:

14.0, 14.1, 14.5, 13.2, 11.2, 14.0, 14.1, 12.2, 11.1, 13.7, 13.2, 16.0, 12.8, 14.4, 12.9

Do these data provide sufficient evidence at the .05 level of significance that the population mean is not 12 ml? What assumptions are necessary?

1. Start SPSS
2. Click Variable View tab
3. Create variable milliliters

1. Click Data View tab
2. Enter data above

1. Click Analyze -> Compare Means -> One Sample t Test
2. Enter test value of 12
3. Interpret the results in APA style.

Rosner Example 10.6: Contingency Table

An investigator had data relating the effect of OC use on heart disease for 15,000 women aged 40 to 44 years. The investigators learned that among 5000 current OC users at the start of the study, 13 experienced a myocardial infarction (MI) during the next three years; among 10,000 nonusers of OCs, 7 experienced a MI during the next three years. See discussion on page 358, Example 10.8.

RQ: Is there a relationship between oral contraceptive use and myocardial infarction?

Step 1: Create Variables

1. Start SPSS.
2. Click the Variable View Tab.
3. Enter the variables MIstatus , OCuse , and frequency.
4. Click the values cell column.

1. Click the push button ellipsis.
2. Enter 1 to the right of value and MIstatus to the right of label; enter 1 =
   Yes and 2 = No.
3. Click Add.
4. Enter 2 to the right of value and OCuse to the right of label;

enter 1 = User and 2 = Non-user.

Step 2: Create the Data

1. Click the Data View tab.
2. Enter the values.

   Mlstatus	OCuse	Frequency
   1	1	13
   1	2	7
   2	1	4987
   2	2	9993

   
   Step 3: Analyze the Data
   I. From the menu bar, select Data>Weight Cases.
   2. The Weight Cases dialog box opens; select weight cases by frequency by moving frequency into the Frequency Variable box.
   3. Click OK.
   4. The Crosstabs dialog box opens;
   1. Select OCuse and move it into Row(s) box.
   2. Select Mistatus and move it into Co/um/3(s) box.
   3. Click the Statistics button; in the Crosstabs: Statistics dialog box, click Chi-square, Risk, and Cramer's V.
   4. Click Continue.
   5. Click Cells: under Counts, select Observed and Expected and under Percentages select Row.
   6. Click Continue.
   7. Click OK.

Step 4: Interpret the Results: Chi square [continuity correction] = Relative Risk = 95% Confidence Interval =

Summary of Results in APA Format:

Daniel 7.4.5

Porcellini et al. investigated the effect on CD4 T cell count of administration of intermittent interleukin (IL-2) in addition to highly active antiretroviral therapy (HAART). The following table shows the CD4 T cell at baseline and then again after 12 months of HAART therapy with IL-2. Do the data show a significant change in CD4 T cell count at the .05 level of significance?

Rosner Example 10.4: Contingency Table

An investigator had data relating the period of time from menarche until first childbirth and breast cancer for 13,465 women. The investigators set up a case-control study. In the following distribution of data, the data in Table 10.1 on page 357 have been arranged so that data for breast cancer status are in the columns and data for age-at-first birth are in the rows.

RQ: Is there a relationship between the age at age of first childbirth and breast cancer?

Step 1: Create Variables

1. Start SPSS.

2. Click the Variable View Tab.

3. Enter the variables BreastCA ,

4. Click the Values cell column.

1. Click the push button ellipsis to open the Values Label box.
2. Enter 1 to the right of Value and enter 1 = Yes. Click Add. Enter 2 to the right of Value and enter 2 = No. Click Continue.

5. Repeat the process with the variable AgeFirstBirth with 1 = 30 or more years and 2 = Under 30 years. Click OK.

6. Enter the variable Frequency as a numeric variable.

Step 2: Create the Data

1. Click the Data View tab.
2. Enter the values.

   Breast Cancer	Age: First Birth	Frequency
   1	I	683
   		2537
   2	1	1498
   2	2	8747

   
   Step 3: Analyze the Data
   1. From the menu bar, select Data> Weight Cases.
   2. The Weight Cases dialog box opens; select weight cases by Frequency by moving frequency into the Frequency Variable box.
   3. Click OK.
   4. The Crosstabs dialog box opens;
   1. Select AgeFirstBirth and move it into Row (s) box.
   2. Select BreastCA and move it into Column(s) box.
   3. Click the Statistics button; in the Crosstabs: Statistics dialog box, click Chi-square, Risk, and Cramer's V.
   4. Click Continue.
   5. Click Cells: under Counts, select Observed and Expected and under Percentages select Row.
   6. Click Continue.
   7. Click OK.

Step 4: Interpret the Results

Chi square [continuity correction] =

Odds Ratio = and 95% Confidence Interval =

Summary of Results in APA Format:

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