# Zach’s facts

Zach’s facts have been extracted from the book to remind you of the key concepts you and Zach have learned in each chapter.

Zach's Facts 11.1 Effect sizes

• An effect size is a way of measuring the size of an observed effect, usually relative to the background error.

• Cohen’s d is the difference between two means divided by the standard deviation of the mean of the control group, or a pooled estimated based on the standard deviations of both groups.

• Pearson’s correlation coefficient, r, is also a versatile effect size measure. It quantifies the relationship between two variables and can lie between −1 (a perfect negative relationship) and +1 (a perfect positive relationship). Zero indicates no relationship at all between variables.

• The odds ratio is often used as an effect size for categorical data. It is the ratio of the odds of an event occurring in one group compared to another. An odds ratio of 1 indicates that the odds of a particular outcome are equal in both groups.

• Meta-analysis is where effect sizes from different studies testing the same hypothesis are combined to get a better estimate of the size of the effect in the population.

Zach's Facts 11.2 Bayesian analysis

• Bayesian analysis uses Bayes’ theorem to evaluate the probability of a theory given the data collected.

• In Bayesian analysis, the scientist’s prior beliefs in a hypothesis are updated using the observed data.

• Bayesian hypothesis testing is based on looking at the probability of the alternative hypothesis given the data and comparing this to the probability of the null hypothesis given the data. This ratio is the posterior odds.

• The Bayes factor is the ratio of the probability of the data given the alternative hypothesis to that for the null hypothesis. A Bayes factor less than 1 supports the null hypothesis, and one greater than 1 suggests that the observed data are more likely given the alternative hypothesis than the null. Values between 1 and 3 are considered evidence for the alternative hypothesis that is ‘barely worth mentioning’, values between 3 and 10 are considered evidence for the alternative hypothesis that ‘has substance’ and values greater than 10 are strong evidence for the alternative hypothesis.79