Do Age, BMI, and History of Smoking play a role? tuberculosis Do Age, BMI, and History of Smoking play a role?

The physical characteristics were recorded of 304 healthcare workers who perform pulmonary bronchoscopies and are suspected to have contracted pulmonary tuberculosis from improper precaution during the procedures.

Hypotheses objectives To explore if there is any correlation or linear relationship between the Body Mass Index (BMI) and the Age of the workers To examine if Tuberculosis and Smoking are independent of each other To determine if the BMI population mean between three levels of smoking history are statistically different

Correlation and Linear Regression model of BMI and Age First Hypothesis Correlation and Linear Regression model of BMI and Age Pearson Correlation Coefficients, N = 304   BMI Age -0.00400 The Pearson correlation coefficient, r, is only -0.004, which means that the two variables Age and BMI are very weakly correlated. The slope of the linear regression model is -0.0007, which suggests as one increases a year in age, one’s BMI lowers by -0.0007, starting from age 0 at the y-intercept of 21.89, however because of the low correlation value, this model does not explain the variance in data well.

Chi Square Test: TB versus smoking Second Hypothesis Chi Square Test: TB versus smoking Table of Smoking by TB Smoking TB 1 Total 86 28.29 47.78 59.31 94 30.92 52.22 59.12 180 59.21   27 8.88 52.94 18.62 24 7.89 47.06 15.09 51 16.78 2 32 10.53 43.84 22.07 41 13.49 56.16 25.79 73 24.01 145 47.70 159 52.30 304 100.00 H0: That Tuberculosis Diagnosis and History of smoking are independent HA: That Tuberculosis Diagnosis and History of smoking are not independent SAS calculated the test statistic χ2= 0.990 and the P-value, P(χ2>0.990)=0.6068. At the 0.05 significance level, one should not reject the null hypothesis (as 0.6068 > 0.05.) In conclusion, the chi-square test indicates that Tuberculosis Diagnosis and Smoking history are independent of each other.

ANOVA Test: Smoking Versus BMI third Hypothesis ANOVA Test: Smoking Versus BMI Source DF Sum of Squares Mean Square F Value Pr > F Model 2 10.616569 5.308284 0.60 0.5492 H0: The mean BMI for all levels of smoking history (never, past, and current) are equal. HA: At least two of the mean BMI’s for all levels of smoking history (never, past, and current) are not equal. SAS calculated a test statistic of F= 0.60 and a P-value of P(F>0.60)=0.50492. At the 0.05 significance level, one would not reject the null hypothesis (because 0.5492 > 0.05.) Thus, one cannot reject that the mean BMI for all levels of smoking history (never, past, and current) are equal. One can conclude that the population means are not statistically different.

Conclusion By testing for correlation, linear relationships, independence, and difference in means, one can begin to make inferences about this data set. From observing Pearson’s correlation coefficient, it was concluded that Age and BMI were weakly correlated. From the chi-square hypothesis test, it was determined that Smoking History is independent of TB, and thus past smoking has no significant effect on contracting TB. From the ANOVA table, it was established that the mean BMI for all levels of smoking history (never, past, and current) are equal. Thus, one can better understand how the three variables of Age, BMI, and Smoking History interact with TB and with each other.