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# Statistical Reasoning

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. Tey are expressed in terms of intervals and the degrees of confidence. Te 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. Dscriptive and inferential statistics can be used together in cases where a sample is used to represent a larger population. I someone is interested the exam marks of all students in the USA, fr example, tey have to use a smaller sample to represent the whole group.

Smple properties like mean, mde 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. I most research conducted on populations, bth descriptive and inferential statistics are used to analyse and draw conclusions from the results. Acording to Chance & Allan (2005), te number of degrees of freedom in statistics the number of values that are free to vary in the final calculation.

Dgrees of freedom are necessary when using the student t-score table where the probability distribution depends on the sample size. Tey are also necessary in the utilization of a chi-square distribution where the sample size determines which distribution to use. Tey also show up in the formula for the standard deviation where average deviation is derived from the mean. Oher advanced statistical techniques that require the use of degrees of freedom are for instance F-test. conducting tere 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).

Pst hoc analysis involves the observation of the data for patterns that were not specified a priori after the experiment has been concluded. Te post hoc analyses are concerned with finding relationships and patterns that would otherwise remain undiscovered and undetected between sampled populations and sub-groups. Tese tests greatly expand the capability and range of methods that can be useful in exploratory studies. also strengthen induction by restraining the likelihood of considerable effects being revealed between subgroups of populations when they don’t exist.

Tey are important procedures. ..

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