Understanding Statistics

Guide to Interpreting Statistics

1. Interpreting Statistics: Introduction

As a teacher, you will not typically be expected to conduct your own statistical tests. When reading background research, however, you may encounter quantitative research in which other authors have used statistics to determine their findings.

This is an advanced guide to help you interpret the statistical tests used by others. The guide will take you through notation used in statistics, some commonly statistical tests, and a quiz to test your own interpretation of the statistics used in other research. If you are a complete newby to statistics, never fear: we provide some additional resources for you to review. A good research paper will also help you: by summarising the results and their implications in the abstract and at the beginning of the discussion.

3. Statistical Tests

The most common tests you will come across are t-tests, analyses of variance (ANOVA) and chi—squared tests. These tests are used to calculate a test statistic such as t, F and χ², which is then converted to a p-value using conversion tables or a computer program. P-values give us the most valuable information about the study by portraying how likely it is that your results have occurred by chance.  Generally, p values of less than 0.05 (p < 0.05) are considered non-random or statistically significant, allowing you to reject the null hypothesis.  However, this figure is set by the researcher and can therefore vary.  Some common tests are tabulated below:

4. Test Statistics

In journal articles, your test statistic will usually appear followed by numbers in brackets.  This represents the number of participants or the degrees of freedom- don’t panic! The information that is valuable to you comes after the equals sign. Some examples include:

• Example 1: F(1, 39) =7.99   ß the test statistic here is 7.99
• Example 2: t(25)=2.05 ß the test statistic here is 2.05 

Correlation coefficients (r) and regression coefficients (b/β) will lie between -1 and 1.  The closer the value to -1 or 1, the stronger the relationship, values closer to 0 represent a weaker relationship. The same rules apply to both correlation and regression coefficients. Come examples include:

• Example 1: When height and weight are correlated, r=0.8, meaning there is a strong positive relationship; as height increases so does weight
• Example 2: When exercise frequency is correlated with resting heart rate, r=-0.8, meaning there is a strong negative relationship; as frequency of exercise increases, resting heart rate decreases
• Example 3: When height is correlated with IQ, r=0.1, meaning there is a weak positive relationship.  As height increases, there is no obvious change in IQ.  If the study was repeated, it is possible that a weak negative ‘r’ value could be obtained.

5. Effect Size

While test statistics converted to p-values are used to tell us whether or not there is a statistically significant difference between our data groups or a significant relationship, effect size is a measure of practical significance used to provide information about how big the difference or relationship is.

It is important to remember that significance and meaningfulness are different. We consider effect sizes because they tell us, relatively, how practically important the finding is and where we might see the largest effects.

Practice Decoding Results Sections

This quiz has three (3) questions and will help you determine your ability to undestand the results sections of various studies. There are no final grades, it’s just for you to practice. Give it a try!