Two groups are tested for anemia. Which test should be used ?
Ans. is `c' i.e., Chi-square test Observations in the given question are in the form of qualitative data (anemia present or not). Thus Chi-square test should be used. Chi square test Is used when the observation are in the form of propoions (for qualitative data) The outcome are in clear cut answers; yes or no. As in the example the HBsAg is either present or not present. In contrast when the observation is normally distributed in the population e.g blood pressure, blood sugar ; student test is used. In the example comparing the occurence of hepatitis B surface antigen in medical and dental students, use of chi square analysis is appropriate because the outcome variables are dichomatous. Students are classified by the presence or absence of HBsAg. Student t test is used when the outcome variable is normally distributed in population (for quantitative data) e.g blood pressure, blood glucose. In the example student t test is used to assess the difference between mean systolic pressure of pregnant and non pregnant women ( to know the effect of pregnancy on mean systolic blood pressure) because mean systolic blood pressure is normally distributed in the population. Every single lady has a mean systolic blood pressure. It may be low or high , but she has a value of mean systolic blood pressure. Students t test may be following types: Unpaired t test (Independent t test) : It compares the mean of two small samples: The data is unpaired from two independent sample. for example, blood sugar concentration is measured in two different group (A group of 10 patients and other group of 8 patient). To test the significance of difference between the means of the two groups, unpaired t test is used. Paired t test : It compares the mean in paired data, before and after the intervention from same sample. For example, Blood sugar level in a sample of 10 patients is measure before giving and after giving the oral hypoglycemic. In this condition paired t test is used. Chi-square test Vs Student t test In the example student t test is used to assess the difference between mean systolic pressure of pregnant and non pregnant women ( to know the effect of pregnancy on mean systolic blood pressure) because mean systolic blood pressure is normally distributed in the population. Every single lady has a mean systolic blood pressure. It may be low or high , but she has a value of mean systolic blood pressure. But suppose we change the example in a way that we make a clear cut definition of hypeension ( such as mean systolic blood pressure over 140 mm of Hg will be taken to be hypeension) and then look for hypeension among pregnant and non-pregnant women. The test now used to analyse the outcome will be chi square test since the outcomes are now in the form of dichomatous data i.e yes or no (a woman is either hypeensive or not hypeensive. This is in contrast to mean systolic blood pressure which was normally distributed among ladies; every lady had one value of mean systolic blood pressure). Analysis of Variance (ANOVA) (F test/ F ratio) ANOVA is considered as an extension of the student t test for the significance of the difference between two sample means. The student t test can be used only for making just one comparison (between two sample means), or between a sample mean and hypothesized population mean. ANOVA is used when more than one comparison is to be made (When means of more than two groups are being compared). For example, BP is measured in more than two groups of men (married, unmarried, widowed, separated and divorced). In this situation ANOVA test is best.
Paired T-test
Unpair T-test
Chi-square test
ANOVA