About this blog

December 24, 2023

Thanks for visiting this blog. Through my many years as a marketing research practitioner, I came across many basic concepts which researchers just don’t know, don’t think about, or just plainly ignore. So, this blog attempts to serve as a quick reference for marketing researchers to selected topics of statistics and marketing research. It also covers some topics of interest to me which I hope will be of interest to you.   [READ MORE]

Thank you I am done!

December 23, 2023

Thanks to all who have kept me busy with your great (and not-so-great) questions since I started this blog 10 years ago. It is time for me to move on to other things. I will continue to keep this blog alive but won’t update it any longer and also sorry to say I will no longer respond to your email questions. I just need to move on to other things in my life. While I love statistics, I now want to dedicate more of my time to stock investing and trading, photography, artificial intelligence, and travel, which take all of my time. I wish you all the [READ MORE]

Repeated Measures ANOVA vs. Linear Mixed Models

May 1, 2023

I recently came across this interesting write-up provided by Karen Grace-Martin. She offers frequent workshops, some of which are free. I highly recommend you follow Karen and consider attending her online workshops. She and her collaborators are brilliant. Check her out at www.theanalysisfactor.com. One of the decisions in statistics that commonly causes confusion for researchers is when to use Repeated Measures ANOVA and when to use Linear Mixed Models. It’s a complicated answer… sometimes you’ll get the exact same result, and sometimes the results will be vastly different. [READ MORE]

Chi-square (χ²) Test of Independence

April 22, 2023

BRIEF DESCRIPTION: Whereas the One-sample Chi-square (χ²) goodness-of-fit test compares our sample distribution (observed frequencies) of a single variable with a known pre-defined distribution (expected frequencies) such as the population distribution, normal distribution, or poisson distribution, to test for the significance of deviation, the Chi-square (χ²) Test of Independence compares two categorical variables in a cross-tabulation fashion to determine group differences or degree of association (or non-association i.e. independence).  Chi-square (χ²) is a [READ MORE]

Data Assumption: Linearity

March 9, 2023

BRIEF DESCRIPTION: Linearity means that mean values of the outcome variable (dependent variable) for each increment of the predictors (independent variables) lie along a straight line (so we are modeling a straight relationship).    Who cares The assumption of linearity is required by all multivariate techniques based on correlation measures of association e.g. Regression, Logistics Regression, Factor Analysis, Structural Equation Modeling, Discriminant Analysis, General Linear Models, etc.    Why it is important Most, if not all of the tests of association / relationships that we [READ MORE]

One-Sample Chi-square (χ²) goodness-of-fit test

February 9, 2023

BRIEF DESCRIPTION: The Chi-square (χ²) goodness-of-fit test is a univariate measure for categorical scaled data, such as dichotomous, nominal, or ordinal data.  It tests whether the variable’s observed frequencies differ significantly from a set of expected frequencies. For example, is our observed sample’s age distribution of 20%, 40%, 40% significantly different from what we expect (e.g. the population age distribution) of 30%, 30%, 40%. Chi-square (χ²) is a non-parametric procedure.   SIMILAR STATISTICAL PROCEDURES: Binomial goodness-of-fit (for binary data) [READ MORE]

Data Assumption: Homogeneity of regression slopes (test of parallelism)

January 19, 2023

BRIEF DESCRIPTION: The dependent variable and any covariate(s) such as in ANCOVA and MANCOVA, should have the same slopes (b-coefficient) across all levels of the categorical grouping variable (factors). In other words, the covariate(s) must be linearly related to the dependent variable. On the other hand, covariate(s) and factors should not be significantly correlated.   Who cares ANCOVA MANCOVA Ordinal regression Probit response models   Why is it important The fact is: when groups differ significantly on the covariate (thus an interaction) then placing the covariate into the [READ MORE]

Variables – three key types

December 10, 2022

Now here’s an easy one: What is a variable? It is simply something that varies – either its value or it’s characteristic. In fact, it must vary. If it does not vary then we can’t call it a VARiable, so we call it a “constant” such as the regression constant (the y-intercept).    In the equation of a straight line (linear relationship) Y = a + bX, where:    Y=dependent variable    X=independent variable    a=constant (the Y-axes intercept, or the value of Y when X=0)    b=coefficient (slope of the line, in other words the amount that Y increases [READ MORE]

Statistical Modeling: A Primer (by Kevin Gray)

November 7, 2022

Interesting article by Kevin Gray at Cannon Gray (http://cannongray.com) Model means different things to different people and different things at different times. As I briefly explain in A Model’s Many Faces, I often find it helpful to classify models as conceptual, operational or statistical. In this post we’ll have a closer look at the last of these, statistical models. First, it’s critical to understand that statistical models are simplified representations of reality and, to paraphrase the famous words of statistician George Box, they’re all wrong but some of them [READ MORE]

How to Analyze Ordinal Variables

October 21, 2022

  I have written a lot about analysing ordinal variables. Here are 5 ways pointed out by Karen Grace-Martin – and she knows well! There are not a lot of statistical methods designed just to analyze ordinal variables. But that doesn’t mean that you’re stuck with few options.  There are more than you’d think. Some are better than others, but it depends on the situation and research questions. Here are five options when your dependent variable is ordinal. 1. Analyze ordinal variables as if they’re nominal Ordinal variables are fundamentally categorical. One simple option is [READ MORE]

Tests of statistical significant can be dangerous and misleading.

September 6, 2022

Years ago we used to programme our IBM PC’s to run t-tests overnight to determine if groups of respondents differ on a series of product attributes. We then highlighted all the attributes with significant differences at p‘<‘.05, p‘<‘.01 and p‘<‘.001 levels and proudly reported to the client which attributes are differentiating and which not. However, after all these years this practice (in many different forms) is still continued by some researchers (though now calculated in a split second), and in total disregard to the validity of a [READ MORE]

Which test: Compare TWO DEPENDENT groups (Paired, Matched, Same respondent groups)

August 3, 2022

When the research objective is to compare two dependent groups, which means they are paired, matched, and thus the same respondent groups in a pre- post-test, we have a choice among different statistical procedures, depending on the following variable characteristics:   Number of variables:  One dependent variable and one independent categorical variable (two levels or groups)   Examples:  Are the means / frequencies (on the dependent variable) of the same respondents over two different time periods significantly different such as in a pre- post test? Are [READ MORE]
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