Question

Suppose you have been approached to design a survey, collect data and then do a statistical analysis from the collected data in any of the public or private sectors in the economy of the Sultanate of Oman.

Group the variables (and the hypothesized relationships of those variables) in three sets so that within each set there is a relationship among the variables you are interested to investigate. The grouping of variables in those three sets should be done in such way as to be able to apply the following non-parametric tests (a different test be applied to a different set of variables):

1) McNemar’s

2) Chi-square Test of Homogeneity

3) Friedman’s Test (Randomized block design)

Note that no data is required in any of the above cases, but you need to suggest a sample size in each case so that the number of degrees of freedom for the chi-square test statistic involved can be determined.

Answer 1

From the given data,

1) McNemer's test is applied on 22 contingency table, where rows and columns marginal frequency must be equal.

Null hypothesis contains the two marginal probabilities for each outcome are equal whereas alternate hypothesis contains they are not equal.

2)

Chi square of homogenity applies on single categorical variable having 2 or more distinct populations.

Degrees of freedom = (Number of rows -1) (Number of columns -1).

Null hypothesis contains each population has the same proportion of observations whereas alternate hypothesis contains they are not having  same proportion.

3)

Friedman's test applied on data having 'n' blocks and 'k' columns to calculate rank within each block.

Degrees of freedom = k-1.

Null hypothesis states medians of all population is same.

Alternate hypothesis states that they are not same