The Question and Why It Is Relevant

        This project addresses the rates of ages and gender for testing positive for the sexually transmitted infection Chlamydia.

        Question: Are the rates of testing positive for Chlamydia for ages and gender independent?

        This question is applicable to both men and women in the United States between the ages of 15-29. Knowledge of trends of the infection would help make the focus of sexual education more effective based on age group and gender.

        Null Hypothesis ( H_o): The age of individuals testing positive for Chlamydia is independent of their gender.

        Alternative Hypothesis( H_a):  The age of individuals testing positive for Chlamydia is dependent on their gender.

How the Data Were Collected

        The data was taken from the Centers for Disease Control and Prevention website <http://www.cdc.gov/page.do> . Annual reports, including tables, statistics, and graphs, were provided. These reports included the rates of testing positive for Chlamydia, as well as the number of cases, for different ages and genders. For these calculations, the rates were used rather than the number of cases due to the nature of the test.  The sample data was collected using random sampling techniques at various testing sites throughout the United States. The sample included 100,000 individuals, which was taken in 2004, the most recent year recorded.

How the Data Were Analyzed

        The data were analyzed using a Chi Square test for independence. The Chi Square test was chosen because we are looking for a relationship between age and gender, with regards to testing positive for Chlamydia. Assumptions necessary for this test are observed counts from a random sample and a large sample size (all expected counts are greater than or equal to 30). The data provided was from a random sample, and all calculated expected counts were greater than 30. Thus, all of the assumptions are met. Rejection of the null hypothesis was determined by comparing X² sample test statistic and the X² critical value.

Results

        The first calculation was the expected rates. This was determined by using the following formula:

        Expected # = [Row Total*Column Total]/ Grand Total

        The following chart shows data used for the calculations:

Table 1. Observed and Expected Counts

[The numbers in parentheses are expected values; the numbers not in parentheses are observed values.]

We then calculated the X² critical value distribution using Table 8 in Appendix B of Just the Essentials of Elementary Statistics, Robert Johnson and Patricia Kuby, Thomson Brooks/Cole, 9th, 2005. Degrees of freedom were calculated using the following formula:

Degrees of Freedom = (Number of Rows -1)*(Number of Columns -1) = (3-1)*(2-1) = 2

Using a level of significance of 0.05 and the calculated degrees of freedom, the X² critical value was determined to be 5.99.

Next, we calculated the X² test statistic using the following formula:

X² _sample = S[(Observed value - Expected value)²/ expected value]

        = (458.3 - 643.3)²/643.3 + (2761.5 - 2576.5)²/2576.5 + (744.7 - 674.4)²/674.4 + (2630.7 - 2701)²/2701 + (420.9-288.2)²/288.2 + (1039.5 - 1154.2)²/1154.2

        = 53.2 + 13.3 + 1.82 + 7.33 + 45.6 + 11.4 = 132.65

X² _sample > X² _critical, therefore, we can reject the null hypothesis.

Implications to Original Question

        Because X² _sample > X² _critical, we rejected the null hypothesis. This means that the age of individuals testing positive for Chlamydia is not independent of gender. The rate of women ages 15-19 and 20-24 are significantly greater than the rates of women ages 25-29 and men ages 15-29.

Appendix

See Table 1 for data set.