Why do epidemiologists calculate chi square tests

Many epidemiologists that our goal should be estimation rather than testing. According to that view, hypothesis testing is based on a false premise: that the purpose of an observational study is to make a decision reject or accept rather than to contribute a certain weight of evidence to the broader research on a particular exposure-disease hypothesis.

Furthermore, the idea of cut-off for an association loses all meaning if one takes seriously the caveat that measures of random error do not account for systematic error, so hypothesis testing is based on the fiction that the observed value was measured without bias or confounding, which in fact are present to a greater or lesser extent in every study.

Confidence intervals alone should be sufficient to describe the random error in our data rather than using a cut-off to determine whether or not there is an association. Whether or not one accepts hypothesis testing, it is important to understand it, and so the concept and process is described below, along with some of the common tests used for categorical data. When groups are compared and found to differ, it is possible that the differences that were observed were just the result of random error or sampling variability.

Hypothesis testing involves conducting statistical tests to estimate the probability that the observed differences were simply due to random error.

Aschengrau and Seage note that hypothesis testing has three main steps:. This procedure is conducted with one of many statistics tests.

The particular statistical test used will depend on the study design, the type of measurements, and whether the data is normally distributed or skewed.

The end result of a statistical test is a "p-value," where "p" indicates probability of observing differences between the groups that large or larger, if the null hypothesis were true. However, this criterion is arbitrary. The ratio of p 1 and p 2 -- the proportion ratio -- is often referred to as the risk ratio or relative risk:.

Thus, rr represents the risk ratio estimate and RR denotes the risk ratio parameter. As an example we consider a cohort of cancer patients undergoing bone marrow ablation with the drug cytarabine Jolson, et al, One group is exposed to i.

Risk ratio estimates are printed in the output below the 2-by-2 table. For the illustrative example:. The confidence interval assumes data are free of biases. Since this is unrealisticthe confidence interval should be viewed as a rough estimate of the parameter. These are:. Chi-Squares P-values Uncorrected: 9. Interpretation: Some statisticians use benchmarks to help interpret the p value. Benchmarks of. Thus, each of the above p values provides evidence against H 0. More importantly, the p value should NOT be interpreted in isolation -- it should be interpreted in light of other evidence Fisher, Assumptions: Chi-square tests, assume data are valid no information bias, no selection bias, no confounding.

They also assume sampling independence and expected frequencies greater than or equal to 5. When an expected frequency in the cross-tabulation is less than 5, Epi Info issues the warning: An expected value is less than 5; recommend Fisher exact results. Fisher's exact test is based on summing exact binomial probabilities for permutations that are equally or more extreme than observed results, assuming the null hypothesis is true and the table's margins are fixed.

This procedure is explained in Rosner, , p. Illustrative Data. To illustrate Fisher's test, let us consider a study performed to explore the relation between a drug called Kayexelate R and the occurrence of colonic necrosis in post-operative patients Gerstman et al. This study compares colonic necrosis rates in postoperatively exposed- and non-patients.

The corresponding Alternative Hypothesis states that the opposite is true, that exposure or risk factor of interest is associated with disease. If by statistical testing the null hypothesis is shown to be statistically implausible or false then it is rejected in favour of the alternative hypothesis that states that the exposure is associated with disease.

The most common statistical test for determination of the p-value for data in a two-by-two standard table is a chi-square test. A very small p-value indicates that statistically the observed association occurs only very rarely if the null hypothesis is true. Before conducting the analysis, the investigator specifies a cutoff in terms of the level of significance in order to accept or reject the null hypothesis.

Other degrees of statistical significance could be selected but must be specified in advance of the calculations. In a epidemiological investigation one should consider the consequences of making and error in a decision about accepting or rejecting the null hypothesis.

You may be right or wrong. An exposure is or is not causally related to disease. A p-value could be larger or smaller than the specified cutoff for statistical significance. A calculation may find a p-value such that the investigator fails to reject the null hypothesis, which may turn out to be true, but could itself be a chance finding rather than a true explanation of an outbreak.

In conducting a chi-square test of statistical significance, one must first develop the hypothesis for testing. Calculate the chi-square statistic. Then using Chi-Square Tables look-up the corresponding p-value for the probability estimate, to determine if it is greater than the specified level of statistical significance.

For example, a two-by-two table has 1 degree of freedom; from the Chi-Square Tables a chi-square value larger than 3.

In a public health epidemiological investigation one should consider the consequences of making and error in a decision about accepting or rejecting the null hypothesis. The confidence interval as often applied in epidemiological studies provides an estimate of the range of values of the risk ratio consistent to the data in a particular study and the variance in the data.

A wide range of values indicates a greater amount of variance in the data and a lack of precision in the strength of the association RR between the exposure and the risk of disease. The main assumption of this group of methods is that for any observation it can only belong to one cell in the contingency table. Row and column totals marginal totals are used to predict what count would be expected for each cell if the null hypothesis were true.