Effect Size

Getting the hang of z-scores

January 4, 2017

If we have a sample of data drawn randomly from a population with a normal distribution, we can assume that our sample distribution also has a normal distribution (provided a sample size of more than 30). If we have a mean of zero and a standard deviation (SD) of 1, then we can calculate the probability of getting a particular score based on the frequencies we have. To centre our data around a mean of zero, we need to subtract each individual score from the overall mean, then divide this by the standard deviation. This is the process of standardisation of raw data into z-scores. This [READ MORE]

Test statistics and significance

November 27, 2016

A test statistic such as the F-test, t-test, or the χ² test, all look at the proportion of variance explained (effect) by our model versus variance not explained (error) by our model. Our model can be as basic as a mean score which is calculated as the sum of the observed scores divided by the number of observations included. If this proportion is >1, then the variance explained (effect) is larger than the variance not explained (error). The higher this proportion the better our model.    Lets say it is 5 (rather than 1), so the proportion of explained variance (effect) is 5 times [READ MORE]

Statistical Power Analysis

July 15, 2016

(Statistical) Power Analysis refers to the ability of a statistical test to detect an effect of a certain size, if the effect really exists. In other words, power is the probability of correctly rejecting the null hypothesis when it should be rejected. So while statistical significance deals with Type I (α) errors (false positives), power analysis deals with Type II (β) errors (false negatives), which means power is 1- β Cohen (1988) recommends that research studies be designed to achieve alpha levels of at least .05 and if we use Cohen’s rule of .2 for β, then 1- β= 0.8 (an 80% [READ MORE]

Practical significance and effect size measures

June 26, 2015

If statistical significance is found (e.g. p<.001), the next logical step should be to calculate the practical significance i.e. the effect size (e.g. the standardised mean difference between two groups), which is a group of statistics that measure the magnitude differences, treatment effects, and strength of associations. Unlike statistical significance tests, effect size indices are not affected by large sample sizes (as in the case of statistical significance).    As effect size measures are standardised (units of measurement removed), they are easy to evaluate and easy to [READ MORE]

Tests of statistical significant can be dangerous and misleading

February 27, 2013

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]

Measuring effect size and statistical power analysis

October 3, 2012

Effect size measures are crucial to establish practical significance, in addition to statistical significance. Please read the post “Tests of Significant are dangerous and can be very misleading” to better appreciate the importance of practical significance. Normally we only consider differences and associations from a statistical significance point of view and report at what level e.g. p<.001 we reject the null hypothesis (H0) and accept that there is a difference or association (note that we can never “accept the alternative hypothesis (H1)” – see the [READ MORE]