A Simple Method for Generation of Statistical Tables by the Help of Excel Software

: A simple and easy method is employed to construct complete statistical tables like Student’s t-distribution, F distribution, Chi-square distribution and Cumulative standard normal distribution in Excel software which are used in all fields of research. Also, we generate other statistical tables like Cumulative binomial distribution, Cumulative Poisson distribution, Fisher transformation and Fisher inverse transformation. The proposed method depends only on the Excel software; it does not depend on the traditional statistical tables.


Introduction
Statistical tables are very important issues in data analysis because whenever the researchers want to test their hypothesis, they need a critical value which is available in the statistical tables. Now a days, Software's are very helpful to all the researchers or the experimenter to solve their problems within the seconds. In this paper, we construct statistical tables like Student's t-distribution, F distribution, Chisquare distribution and Cumulative standard normal distribution which are mostly used in all the fields of research. There have already been proposed various statistical tables to investigate the hypothesis according to the situation e.g. Gosset (1908) developed Student's t-distribution, Snedecor (1934) proposed F distribution, according to Chaudary (1996) the chi square distribution was first obtained in 1875 by Helmert and De Moivre (1738) worked firstly on the Normal distribution but no software is available to present all the values of a table at the same time. Each statistical software provides only one critical value at one time. In this paper, we construct the complete statistical tables using the statistical functions which are available in the Excel.
The rest of the paper is ordered as follows. The next section reviews the methodology; the third section presents the results and discussion and finally, concludes the study.

Methodology
In this section, four statistical distributions are described briefly which are used in our study. Gosset (1908). Student was the pen name in the student's t distribution. The t-distribution is used for small sample size and applied in statistical inference specially. The distribution depends upon only one parameter. Table 1 gives the concise use of Student's t test. A Student t-distribution is defined by the density function as:

Student's t-distribution: Student's t-distribution was developed by
Where the beta function, x is the variable and v is the parameter.

F-distribution:
To test the hypothesis of the differences between two means when variances are equal then we used t-distribution but in many times the variance are not equal, to check this assumption we used F-distribution. F-distribution was proposed by Snedecor (1934). This distribution depends upon two parameters, namely 12 v and v degrees of freedom in the numerator and degrees of freedom in the denominator respectively.
The probability density function of F-distribution depends only on the degrees of freedom in the numerator and degrees of freedom in the denominator respectively.
Chi square ( 2 )-distribution: The chi-square distribution was first developed by Helmert in 1875.
The 2 distribution has only one parameter which is called the number of degrees of freedom. Table 2 present the brief use of the 2 distribution. A 2 distribution is defined by the density function has the following form in equation (3) The density function of Chi-square distribution depends only on the degree of freedom n.  Where is the mean, is the standard deviation, and e are constants values are equal to 3.1416 and 2.7183 respectively. Normal distribution has two parameters say and also the density function of normal distribution depends upon and .

Results and Discussion
To generate the t-distribution table, we have to need the degrees of freedom and the probability values which is denoted by the in the right hand tail. Formulas must begin with an equal sign "=" in Excel. In Excel, we used the formula = TINV (probability, deg_freedom) to construct the t-distribution table and Excel will return the inverse of the t-distribution. Here, probability means the critical values say and deg_freedom means the degree of freedom. First of all, we choose the different critical values e.g. 0.0005, 0.001, 0.005, 0.01, 0.025, 0.05, 0.1, and 0.2 and secondly taking the degrees of freedom which starts from 1, 2, 3 and so on. Suppose for 0.05, firstly we write the critical value 0.05 and secondly write the degrees of freedom say 1 in the above function and drag up to the requirement. Same procedure adopt for the other critical values. See Table 4 for complete t-distribution table for all critical values which are assumed in our study. Our calculated table values are similar with the traditional tables like Montgomery (1984) and Larry (1998).
To generate the F-distribution table, we have to need the degrees of freedom in the numerator say 1 v and the denominator say 2 v respectively and the probability values which is denoted by the . In Excel, we used the formula = FINV (probability, deg_freedom 1, deg_freedom 2). Here, probability means the critical values which you have required say and deg_freedom 1 means the degree of freedom of the numerator and the deg_freedom 2 indicate the degree of freedom of the denominator. Excel will return the inverse of the F-distribution. First of all, we choose the critical value e.g. 0.1 and secondly taking the degrees of freedom of 1 v and 2 v which starts from 1 and 1 respectively and drag up to the requirement.
See Table 5 in appendix for complete F-distribution table for 1% critical value which is assumed in our study.
To produce the 2 distribution table, we have to need the degrees of freedom and the probability values which is denoted by the . In Excel, we used the formula = CHINV (probability, deg_freedom) and Excel will return the inverse of the one tailed probability of 2 distribution. First of all, we choose the critical values e.g. 0.995, 0.990, 0.975, 0.950, 0.900, 0.100, 0.050, 0.025 and 0.010 and secondly taking the degrees of freedom starts from 1 and so on and drag up to the requirement. See Table 6 in appendix for complete 2 distribution table for the selected critical values which is assumed in our study.
To build the cumulative standard normal table, just we have to need the z values and the probability values which is denoted by the . In Excel, we used the formula = NORMSDIST (z) and Excel will return the probability from to a particular point say x (i,e. () P X x ). We select the critical values e.g. 0, 0.01, 0.02, 0.03, 0.04, 0.05 and 0.06 and secondly taking the Z values e.g. -3.7 up to +3.7. See Table 7 in appendix for complete cumulative standard normal distribution for the selected critical values which is assumed in our study.
In the end, we also generate others statistical tables like Cumulative binomial distribution, Cumulative Poisson distribution, Fisher transformation and Fisher inverse transformation. For Cumulative binomial distribution, we used the statistical function of = BINOMDIST (number_s, trials, probability_s, cumulative).
Here, in the above syntax number_s indicates the number of trials (must be integer), trials means the independent trials, probability_s shows the probability of success and two options are available in Excel for cumulative one is false and the other is true, If we use false then Excel will return the mass function and if we write true then it will return the cumulative distribution function. To draw the Cumulative Poisson distribution table, we employed = POISSON (x, mean, cumulative). Here, in the above syntax x indicates the number of events (must be integer), mean is the expected numeric value and cumulative operates the same as in Binomial distribution. See Table 8 & 9 for cumulative binomial and Poisson distribution. For Fisher transformation and Fisher inverse transformation (tables are not reported in our study), we used =FISHER (x) and =FISHERINV (y) where x is a numeric value for which you want the transformation and y is the value for which you want to perform the inverse of the transformation respectively.

Conclusion
In this manuscript, a simple and easy method is used to construct statistical tables like Student's tdistribution, F distribution, Chi-square distribution and Cumulative standard normal distribution in Excel software which are mostly used in all fields of research. The method depends upon only the Excel software; it does not depend on the traditional statistical tables. Also, we develop others statistical tables like Cumulative binomial distribution, Cumulative Poisson distribution, Fisher transformation and Fisher inverse transformation using the statistical functions. This study will hopefully help the researchers to take the decisions about their hypothesis by the help of only Excel software not depend on the traditional statistical tables.