Answer to Question #155781 in Statistics and Probability for Wachira Ann Wangari

Question

Differentiate the following terms as used in categorical data analysis

1) Multinomial sampling vs binomial sampling

2)Poisson sampling process vs probability proportional to size sampling

3) Goodness of fit test vs test of association

4) relative risk vs odds ratio

Answer 1

1) Multinomial sampling may be considered as a generalization of binomial sampling. Data are collected on a pre-determined number of individuals that are units and classified according to levels of a categorical variable of interest.

When the data are collected on a pre-determined number of units and are then classified according to two levels of a categorical variable, a binomial sampling emerges.

2) Poission sampling is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample each element of the population may have a different probability of being included in the sample. If all first-order inclusion probability is equal Poisson sampling becomes equivalent to Bernoulli sampling which can therefore be considered to be a special case of Poisson sampling.

Probability proportional to size sampling is a method of sampling from a finite population in which a size measure is available for each population unit before sampling and where the probability of selecting a unit is proportional to size. Its use arises in two particular contexts multistage sampling and single-stage sampling.

3) The goodness of fit test is a statistical hypothesis test to see how well sample data fit a distribution from a population with a normal distribution. The goodness of fit establishes the discrepancy between the observed values and those that would be expected of the model in a normal distribution case. Test of association in statistics usually means the chi-square test. It's used in an informal sense to mean many things. Any time you are trying to find out if two variables are linked in some way, you are testing for the association. The test of association involves Cochran-Mantel-Haenszel test, fisher's exact test, gamma coefficient test.

4) Odds ratio and relative risk are often confused dispute being unique concepts the basic difference is that the odds ratio is a ratio of two odds whereas the relative risks is a ratio of two probabilities.

The relative risk of an event is the likelihood of its occurrence after exposure to a risk variable as compared with the likelihood of its occurrence in a control or reference group. The relative risk is estimated as the absolute risk with the risk variable divided by the absolute risk in the control group.

The odd ratio is a comparison of the odds of an event after exposure to a risk factor with the odds of that event. In a control or reference situation. The odds ratio is estimated as the odds of an event other than the exposure group divided by the odds of that event in the control or reference book. The result is expressed as a ratio to denominator 1.