In inferential statistics are first the confidence intervals that give ranges of values for unknown parameters of populations through the measuring of the statistical samples. They are expressed in terms of intervals and the degrees of confidence. The other division is the hypotheses testing that tests claims about the populations through the analysis of statistical samples and expressed in terms of levels of significance.Descriptive and inferential statistics can be used together in cases where a sample is used to represent a larger population. If someone is interested in establishing the exam marks of all students in the USA, for example, they have to use a smaller sample to represent the whole group. Sample properties like mean, mode and median are derived from descriptive statistics while estimation of these and other parameters and the testing of statistical hypothesis are reached by inferential statistical analysis. In most research conducted on populations, both descriptive and inferential statistics are used to analyse and draw conclusions from the results.According to Chance & Allan (2005), the number of degrees of freedom in statistics is usually the number of values that are free to vary in the final calculation. Degrees of freedom are necessary when using the student t-score table where the probability distribution depends on the sample size. They are also necessary in the utilization of a chi-square distribution where the sample size determines which distribution to use. They also show up in the formula for the standard deviation where average deviation is derived from the mean. Other advanced statistical techniques that require the use of degrees of freedom are for instance F-test. In conducting this, there are k samples with n size each making the degrees of freedom in the numerator as k-1 and in the denominator as k(n-1).Post hoc analysis involves the observation of the data for patterns that were not specified a priori after the experiment has been concluded. The post hoc analyses are concerned with finding relationships and patterns that would otherwise remain undiscovered and undetected between sampled populations and sub-groups. These tests greatly expand the capability and range of methods that can be useful in exploratory studies. They also strengthen the induction by restraining the likelihood of considerable effects being revealed between subgroups of populations when they don’t exist. They are important procedures
ReferenceChance B. L., Rossman & Allan J. 2005. "Preface". Investigating Statistical Concepts, Applications, and Methods. Duxbury Press.
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