Uses of the Different Tables that are Frequently Used In Statistics

I was stuck when ma’am raised this question: what is the use of the Chi-Square Distribution table? I had my several thoughts but all of it was not correct. Then another thought came into my mind, how about the z-test table? The table F? And the other tables? In what kind of problems should we need to use them?

So now I got to start with my research of the Uses of the Different Tables that are used in Statistics and the results were as follows:

The z-table is short for the Standard Normal Z-Table. The Standard Normal distribution is used in hypothesis tests, including tests on proportions and on the difference between two means. The area under the whole of a normal curve is 1, or 100 percent. The z-table helps by telling us what percentage is under the curve at any particular point. (http://www.statisticshowto.com/articles/what-is-a-z-table-used-for/)

The Standard Normal distribution is used in various hypothesis tests including tests on single means, the difference between two means, and tests on proportions. The Standard Normal distribution has a mean of 0 and a standard deviation of 1. The animation above shows various (left) tail areas for this distribution. For more information on the Normal Distribution as it is used in statistical testing, see Elementary Concepts. (http://www.statsoft.com/textbook/distribution-tables/ )

. A chi square (X²) statistic is used to investigate whether distributions of categorical variables differ from one another. Basically categorical variable yield data in the categories and numerical variables yield data in numerical form. Responses to such questions as "What is your major?" or Do you own a car?" are categorical because they yield data such as "biology" or "no." In contrast, responses to such questions as "How tall are you?" or "What is your G.P.A.?" are numerical. Numerical data can be either discrete or continuous. The table below may help you see the differences between these two variables. (http://math.hws.edu/javamath/ryan/ChiSquare.html)

The Shape of the Student's t distribution is determined by the degrees of freedom. As shown in the animation above, its shape changes as the degrees of freedom increases. For more information on how this distribution is used in hypothesis testing, see t-test for independent samples and t-test for dependent samples in Basic Statistics and Tables. See also, Student's t Distribution. As indicated by the chart below, the areas given at the top of this table are the right tail areas for the t-value inside the table. To determine the 0.05 critical value from the t-distribution with 6 degrees of freedom, look in the 0.05 column at the 6 row: t_(.05,6) = 1.943180. (http://www.statsoft.com/textbook/distribution-tables/ )

Like the Student's t-Distribution, the Chi-square distribution's shape is determined by its degrees of freedom. The animation above shows the shape of the Chi-square distribution as the degrees of freedom increase (1, 2, 5, 10, 25 and 50). For examples of tests of hypothesis that use the Chi-square distribution, see Statistics in crosstabulation tables in Basic Statistics and Tables as well as Nonlinear Estimation . See also, Chi-square Distribution. As shown in the illustration below, the values inside this table are critical values of the Chi-square distribution with the corresponding degrees of freedom. To determine the value from a Chi-square distribution (with a specific degree of freedom) which has a given area above it, go to the given area column and the desired degree of freedom row. For example, the .25 critical value for a Chi-square with 4 degrees of freedom is 5.38527. This means that the area to the right of 5.38527 in a Chi-square distribution with 4 degrees of freedom is .25. (http://www.statsoft.com/textbook/distribution-tables/ )

The F distribution is a right-skewed distribution used most commonly in Analysis of Variance (see ANOVA/MANOVA). The F distribution is a ratio of two Chi-square distributions, and a specific F distribution is denoted by the degrees of freedom for the numerator Chi-square and the degrees of freedom for the denominator Chi-square. An example of the F_(10,10) distribution is shown in the animation above. When referencing the F distribution, the numerator degrees of freedom are always given first, as switching the order of degrees of freedom changes the distribution (e.g., F_(10,12) does not equal F_(12,10)). For the four F tables below, the rows represent denominator degrees of freedom and the columns represent numerator degrees of freedom. The right tail area is given in the name of the table. For example, to determine the .05 critical value for an F distribution with 10 and 12 degrees of freedom, look in the 10 column (numerator) and 12 row (denominator) of the F Table for alpha=.05 (http://www.statsoft.com/textbook/distribution-tables/)

These tables of distributions were made for different purposes of different kind of problems that involves the use of Statistics. Thanks to all those Statisticians that made this tables so that we can be able to go through our calculations in the easier and faster way of it.

Posted by: Kent Spencer Manalo Mendez