Many years ago I developed "PsychoStats", a suite of programs for statistical data analysis (§1).  They were written in BASIC and ran on a Hewlett-Packard 2114B mini computer.  The 2114B was a 16-bit computer with an 8k ferrite core RAM and, as I recall, it ran at 8 MHz with a 2µs cycle time.  Storage was punched paper tape, and the console was an ASR33 teletypewriter which printed at 10 characters per second.

The primary trick of the suite was the calculation of follow-on analyses subsequent to a significant interaction effect in the analysis of variance.  At the time, computer packages for data analysis only provided for the first overall analysis and left it up to the user to calculate simple main effects, simple interaction effects, and pair-wise and multiple contrasts as best they could.  I have recently returned to assisting with data analysis, and to my surprise found this situation essentially unchanged.  SPSS is my favoured software that is accessible to relative novices, and 50 years later it still cannot provide the appropriate analyses following a significant interaction.  Other software packages such as the popular R require the user to be a statistician in order to arrange the necessary calculations.

The following pages provide tutorials and explanations of the workflow needed for complete data analysis using anova techniques.  The treatment I prefer is conceptual, so there are no derivations of formulae, and there is just a small handful of equations that are unavoidable.  I assume an initial general acquaintance with the statistics represented by s, t, F, and r (standard deviation, Student's t, Fisher's F ratio, Pearson correlation coefficient), the concepts represented by N, df, p, α, and 1-β (sample size, degrees of freedom, probability, level of significance, test power), and comfort with the arithmetic procedures represented by x² and √ (square, square root).  The intention is to develop a deeper understanding of the meaning and inter-connectedness of statistical concepts by explaining their use in answering questions about data.  Most uses, certainly in the earlier sections, can be calculated using a spreadsheet app such as Excel.  Relative novices in search of an accessible and thorough textbook need only acquire a recent edition of Andy Field's absolutely superb "Discovering Statistics" (§2).

Basics of one sample:  what you need to know about variance, standard error, and testing the difference between a sample mean and some specific value.

Next:  what you need to know about (1) two independent samples and (2) two dependent samples, testing the difference between two sample means and its connection with correlation and regression.

Analysis of variance basics:  fundamentals of the one way anova and repeated measures.

Two-way anova:  interaction in the two-way analysis of variance with simple main effects and pairwise comparisons.  Three parts, covering (1) Two way factorial anova, (2) Two way repeated measures on one factor, (3)  Two way repeated measures on both factors.

Three-factor anova.

(§1)  Gilbert, L. H. (1979). PSYCHOSTATS: BASIC programs for data analysis in psychology. Behavior Research Methods & Instrumentation, 11(4), 464.  https://doi.org/10.3758/BF03205707

(§2)  Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th edition). Sage Publications.  Andy has an earlier version of "Discovering" that pairs with R for users who do not have access to SPSS.

©2024 Lester Gilbert