Data Summary and Presentations

The more typical descriptive statistical measures: number of data, arithmetic mean, mode, variance, standard error, skewness, kurtosis, quartiles, maximum and minimum are computed.
The same descriptive measures as in Summary.xlsx are computed, but for variables classified in a frequency table.
An easy way to plot a bar and a pie charts.
Setting an anchor point (a bit lower than the minimum of the sample) and an interval width (the template helps the user computing the integer part of  \(\sqrt{n} \)
(being n the number of data), that can be used to fix the number of intervals and, therefore, the binwidth.
Up to four boxplots for different variables can be created.
The regression line of Y over X is computed, along with the coefficient R².
When we have a bidimensional variable in a two-way table format, some different measures are calculated (arithmetic means, variances, covariance and linear correlation), and also the two regression lines (Y over X, and X over Y).
For a two-way table, considering that the different values correspond to qualitative variables, some associate measures are calculated:
-chi-square χ²,
-Yule’s \(Q\) for \(2\times 2\) tables,
-the contingency coefficient \( C=\sqrt{\frac{\chi ^{2}}{\chi ^{2}+N}}\) where χ² is derived from Pearson’s chi-squared test, and\(N\) is the grand total of observations
-the Cramer’s \(V\), given by
\(V= \sqrt{\frac{\chi ^{2}}{N(k-1)}}\), with \(k\) being the number of rows or the number of columns.

Random variables

For a discrete random variable (described by their values and probabilities), the expectation, variance, standard deviation, Pearson’s coefficient of variation, and the coefficient of skewness and kurtosis are computed.
Computes the probability’s law and distribution function, the expectation and standard deviation of the binomial random variable. A bar chart with the probability function is also shown.
The same information as in the previous template is presented here, but for the Poisson distribution.
Similar template to the previous for the case of the negative binomial distribution.
Similar template to the previous considering the hypergeometric distribution.
Considering a exponential distribution, the expectation and variance are computed, and the corresponding density function is drawn. The user can compute probabilities between two values (or probabilities greater or lower than a particular point) and quantiles.
The same information as in the previous template is presented here, but for a Gaussian random variable.
Similar template to the previous one, but for the case of a t-student distribution.
This template works as the previous one in the case of χ² distribution.
The same information is displayed here, but considering a F-distribution.
It gathers all the considered discrete and continuous random variables in the same spreadsheet, allowing to compute probabilities in points (values of the corresponding densitiy for continuous variables), areas between points or quantiles.
The user can explore the Gaussian curve in an interactive fashion. In the first case, the graph contains interactive buttons that allows the comparison of a normal density with different values for the mean and/or the variance with the standard N(0,1) variable. In the second case, the user can learn about the symmetry of the normal density function, by moving the buttons and computing areas under the curve.

Confidence Intervals

For one sample, we can compute the confidence interval for the mean (considering the variance known or unknown) and for the variance (considering the mean known or unknown). In both cases, we can write directly the data in the first column, as well as computing the intervals from summary values (sample size and sample mean, or sample variance).
Confidence intervals for the difference between two means, and for the ratio of variances of two normal variables.
Confidence intervals for a sample proportion, or the difference between two sample proportions.

Hypothesis testing

(Unilateral or bilateral) test about the mean of a normal random variable (where the variance can be known or unknown).
Test about the populational variance (or the standard deviation) of a normal random variable (with the mean known or unknown).
Test about mean differences between two means, and for the ratio of variances of two normal variables.
Test about a proportion.
Test about the difference between two proportions.

Some examples of Templates in a web:


Contingency Table

Confidence intervals for the mean and the variance

Hypothesis testing about the mean of a normal random variable.