Descriptive and Inferential Statistics - Essay Example

Thus, from that sample, the analysis of the sample speaks volumes of the entire population where the sample came from. 

Thus, the difference between these two categories is their functions; descriptive statistics is concerned with the spread and centrality of data whereas inferential statistics is concerned with the generalizability of the data set. As much as the two categories use similar aspects such as mean, standard deviation, the focus of the two is extremely different. Inferential statistics always start with a sample and end up inferring the entire population using similar calculations as that of descriptive statistics.

Descriptive statistics is only useful in cases whereby one does not wish to extend the statistics results to a larger group or population whereas inferential statistics are used when one wishes to make predictions and inferences on a particular population through the observations from the sample. Thus, the two categories can be used together in cases where a data set has to be fully described and inferences or rather predictions from the available observations made.

1. What is a degree of freedom? Why are degrees of freedom important?

Degrees of freedom of any given estimate refers to the number of independent pieces' role of vent information in which all the estimates are based.

Thus, degrees of freedom are crucial in statistics due to the following reason: It is deemed to be a measure of how certain the sample is representative of the whole population. Therefore, when the degrees of freedom are more, the level of certainty in the accuracy of population sampling is high.

In addition, when it comes to fitting models to a given data, degrees of freedom are considered independent parameters. Thus, an accurate model is described by more independent parameters which are a result of more degrees of freedom.

2. Explain what a post hoc test is and why they are important. Provide an example of when you might use a conservative, a moderate, and a very liberal post hoc test. Differentiate between the post hoc tests used in ONEWAY ANOVA and Multiple-Factor ANOVA

A post hoc test refers to an analysis that is performed at the second stage of variance analysis; ANOVA or MANOVA when the null hypothesis is not accepted. This test is meant to determine the groups that significantly differ from the others, the mean under consideration. Post hoc test is sometimes referred to as the data dredging and it operates on the theory that when something is searched for longer periods, it is more likely to be found.

Thus, a post hoc test or rather an analysis is relatively crucial as it assists researchers or statisticians to identify the data that was not specified initially in the data set before the experiment was performed. This test is used to identify and document the data that otherwise would have been left out in the analysis.

Conservative post hoc test is used in circumstances where there is a need of making many complex comparisons of the post hoc. For instance, conservative post hoc analysis is used in cases when the number of post hoc is more than K-1.

The moderate post hoc test is used when one opts to make comparisons that lie between k-1 and (k(k-1))/2.

Finally, a liberal post hoc test is used in situations where there are three means to be compared. Thus, it is not a proper test accumulating means.

One-way ANOVA Post hoc tests and Multiple-Factor ANOVA are used to determine the means that differ in a data set. One-way ANOVA post hoc test identifies the homogenous sets of means that cannot differ from other means whereas the Multiple-Factor ANOVA identifies the difference that exists between each pair of the computed means.

3. Explain the process step by step which you would interpret a significant 3 x 2 test

A 3 x 2 significant test is presented on a table with three rows and two columns. Thus, the results in a 3 by 2 table can be interpreted concerning the tests; means, or variances. For the case of means, the results of the test show the relationship between the means of variables.

The first value in the first row of the result table shows the relationship between the variable on the first column in the first row. Similarly, the second value in the first row of the result table represents the relationship between the second column and the first row variables. The same applies to other rows and columns.