Statistical presentation is the presenting the data for the application of statistical tests such as F-tests, t-tests and chi-square. In the analysis of the data, we include information about the obtained magnitude or value of the test, the probability level, the direction of the effect and the degrees of freedom. In statistical presentation, we include descriptive statistics such as means or medians in the results. In the interpretation of results, we also include an associated measure of variability like standard deviations, variances, or mean square errors. However, we have to justice the use of all tests.
Sufficient statistics means sufficient information. A set of sufficient statistics include cell means, cell sample sizes and some measure of variability like cell standard deviations or variances for parametric tests of location such as single-group, multiple-group, or multiple-factor tests of means. A set of sufficient statistics also comprises cell means and the mean square error and degrees of freedom related to the effect being tested. In case of randomized-block layouts, repeated measures designs and multivariate analyses of variance, a set of sufficient statistics include vectors of cell means and cell sample sizes, along with the pooled within cell variance covariance matrix.
In correlation analyses like multiple regression analysis, factor analysis and structural equations modelling, the sample size and variance covariance matrix are needed along with other information related to the procedure used like variable means, hypothesized structural models, re-liabilities and other parameters.
In case of non-parametric analyses like chi-square analyses of contingency tables, order statistics, sufficient statistics cover various summaries of the raw data like the number of case in each category, the sum of the ranks and sample sizes in each cell. Complete data in a table or figure should be provided for analyses based on very small samples covering single-case investigations.