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Disease patterns or relationships in public health are reached by hypothesis testing in an epidemiological process. Public health has very many issues where the requirement would be to examine the risk exposure in a whole population while the real investigation is possible only in a sample one. The hypothesis of proportion allows us to generalize the results of a sample population to get the picture on the whole.
The process of research may have been initiated to assess the risk of an illness or habit in a population so that measures may be planned and implemented for the whole. The increased incidence of bronchogenic carcinoma or cancer of the lungs is known to have smoking as a causative factor. To reduce the increasing incidence of this malignant illness, the public health authorities would want to detect the incidence of smoking and its various details through a study of the population. For want of time and constraints of cost, the method is to do a random sampling from a section of population and utilize the results to compound the risk for the total population. The inferences would provide useful information and details as to whether gender or race or ethnicity or a specific age group or a specific group by the level of education or a group of workers in an industry or a group addicted to alcohol or drugs has any bearing on the incidence. The public health practitioners and the policymakers would use these results for prioritizing programs and develop policies followed by chalking out a plan for reducing the incidence through various public health measures like information and education to reduce the incidence of smoking and thereby cancer lung. The extent of propaganda and the budget would depend on how high the incidence is or would be and whether any specific group has a predilection to the smoking. Repeat research would show how much the procedure has worked.
A research can have a research hypothesis and a statistical hypothesis. A research hypothesis provides an idea about the clinical question in the population. The statistical hypothesis establishes the basis for tests of significance (Zou, 2003). The hypothesis tests can be used for a single proportion or for comparison of two independent proportions.
The steps to the hypothesis of proportion would be to state the hypothesis, have an analysis plan, analyze sample data and interpret the results. A null hypothesis and an alternative hypothesis are both tested. These two versions would be mutually exclusive and when one is proved true, the other is false (Statistics Tutorials, Stat-Trek).
Sample of hypothesis of single proportion
Fielding et al did research on the helical CT features on ureteral calculi at the Department of Radiology, University of North Carolina at Chapel Hill. The sample consisted of 100 patients. 71 of the calculi were extruded spontaneously (Zou, 2003). The intervention was done for the remaining 29. Literature reveals that 80% of stones smaller than 6 mm. would be passed via the urethra normally (Drach, 1992; Segura, 1997). In Fielding’s study 86% of stones smaller than 6mm (57 out of 66) were passed spontaneously. The statistical hypothesis test is done to check if the finding agrees with the literature findings. 5steps are needed (Zou, 2003).
- H0 80% will pass spontaneously π = 0.80
- H1 The proportion that passes spontaneously. y in the research is not equal to 80%. π ≠ 0.80
This is a two-sided hypothesis.
- The test statistic Z is 1.29 depending on the Z test results of s single proportion.
- The P-value is the sum of the two probabilities of a standard normal distribution where Z is beyond ±1.29.
The analysis plan should specify the significance levels which could be between 0 and 1 and the test could be the one-sample z test. The test statistic and associated P-value are found using the sample data. The P-value is the probability of observing a sample statistic as extreme as the test statistic. The Normal Distribution Calculator can be used to assess the probability associated with the z-score. The results are interpreted thus. The standard deviation of the sample distribution would be σ = sqrt[ P ( 1 – P ) / n ] where P is the hypothesized value of population proportion in the null hypothesis, and n is the sample size
The P-value is 0.20 here. The significance level is lesser at 5%. So H0 is not rejected or the null hypothesis is not rejected (Zou, 2003).
- 80% of stones lesser than 6mm. the width would pass through the urethra spontaneously as said in the literature.
Sample of the hypothesis of two independent proportions
Brown et al believed that the multilocularity or imaging appearances of the two groups of 81 primary ovarian tumors and 24 metastatic tumors were different (Watanabe, 2001). 30 of the first group and three of the second group were multilocular. To detect if the respective underlying proportions were different, a statistical hypothesis test was done (Zou, 2003).
- The difference between the proportions of the multilocular varieties of the two tumors among the primary and secondary tumors is zero (π1, π2 ) or π1 – π2 = 0 or H0 is zero. There is a difference in proportions where H1 = π1 – π2 ≠ 0. This is a two-sided test.
- On the basis of the results of the Z test to compare the two independent proportions test statistic Z is 2.27.
- The P-value 0.02 is the sum of the two tail probabilities of a standard normal distribution where Z is beyond ±2.27 (Zou, 2003).
- H0 is rejected as the P-value of 0.02 is less than the significance level at 5%. This would lead to the inference that there is a statistically significant difference between the multilocular masses with the primary tumors and secondary ones (Zou, 2003).
These methods are used in most scientific researches today: to make conclusions based on probability. In a single proportion the exact binomial is used while in two independent proportions, the large sample Z test which gives values from a contingency table is used (Zou, 2003).
References
Drach, GW. (1992). “Urinary lithiasis: etiology, diagnosis and medical management”. In: Walsh PC, Staney TA, Vaugham ED, eds. Campbell’s urology. 6th ed. Philadelphia, Pa: Saunders, 1992; 2085-2156.
Segura, JW, Preminger GM, Assimos DG, et al. (1997) “Ureteral stones: clinical guidelines panel summary report on the management of ureteral calculi”. J Urol 1997; 158:1915-1921. Statistical Tests. 2009. Web.
Watanabe S, Tsugane S, Sobue T, Konishi M, Baba S.“Study design and organization of the JPHC study. J Epidemiol 2001; 11(Suppl): S3–S7.
Zou, K.H. et al, (2003). “ Statistical concepts series”. RSNA.
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