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1- How would you select appropriate statistical tests for analysis research data? What aspects of research questions or data types are relevant considerations in choosing your tests? Why?
|Following are the factors that must be considered while choosing an appropriate statistical test for analysis of research data: |
|(a) Scale of measurement of the variables (nominal, ordinal, interval or ratio) |
|(b) Any assumptions that may be required regarding the population |
|(c) Number of groups or samples (1, 2 or more than 2) |
|(d) Nature of relationship between the groups (independent or dependent) |
|(e) Number of variables (single or two or more) |
|All the factors are equally important, but the first and the second factor will tell us whether we need to perform a parametric analysis or a nonparametric |
|analysis. If the statistical variable understudy can be represented on a ratio or at least an interval scale of measurement, then it is said to have proper |
|units. With some assumption made about the distribution of the variable (say normality, for example), the variable is fit to be tested parametrically. The |
|t-test, the z-test etc are a few well-known parametric testing methods. Further, these tests can be used to test a single group (single sample) or two groups |
|(two samples). Again, independent and dependent samples are tested using different tests specially designed for them. Means of more than two groups can be |
|tested using ANOVA. But these tests lay different restrictions on the data. |
|If a statistical variable is of the nominal or ordinal type only, then it does not qualify to be parametrically tested. Sometimes we may have obtained a |
|sample which may not be a part of a well-defined population. In this case, there are no population parameters to fall back upon since the population is itself|
|nonexistent or not well defined. Here we conduct a non-parametric test, which is essentially distribution-free. In this case, there are no requirements of |
|normality or homogeneity in the data. |
|The research question may be a one-sided hypothesis or a two-sided hypothesis, and the model should be formulated accordingly. |
|If we are required to an analysis of the relationship between two (or more) variables, then we do regression or χ2- test. Here too, the nature of data plays a|
|decisive role. If both input and output variables are continuous, then we may do regression. If both are attribute type, we may use χ2 tests. The hypotheses |
|statements become slightly different and are worded appropriately depending upon the question being analyzed. |
2- Why is the coefficient of correlation an important tool for statisticians? Provide some specific examples from real life.
|Correlation means “association”- the degree or the extent of relationship between two variables. In correlation analysis, we calculate the correlation |
|coefficient which is a measure of the degree of covariablity between two variables X and Y. Correlation is merely a tool to ascertain the degree of |
|relationship between X and Y. |
|A researcher may be interested in determining the correlation among two or more variables in several real-life situations or in the workplace. For example, |
|one may do correlational research to find out if stress levels are related to number of working hours, or to find out if the performance of students is |
|related to the pocket money that they are given. An event coordinator for the upcoming craft fair may wish to study if there is a connection between |
|attendance at craft fairs and the number of exhibitors who have booths at the fair. Studies can be carried out to examine if there is a correlation between |
|smoking and cancer. Another example would be to analyze if a correlation exists between social status and happiness. Such studies help in understanding if one|
|variable really affects another or not. |
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