first year recap

frequency distribution

• values on the x-axis

• frequencies on the y-axis

normal distribution

• describes a symmetrical plot of data around its mean value

• the width of the curve is defined by the standard deviation

skew

• measure of symmetry of distribution

• 0 = perfect symmetry

• scores clustered at the lower end of distribution = positive skew

• scores clustered at the higher end of distribution = negative skew

kurtosis

• measures the degree to which scores cluster at the tails of a frequency distribution

• positive kurtosis = too many scores in the tails, resulting in a peaked curve

• negative kurtosis = too few scores in the tails, resulting in a flattened curve

central tendency

centre of a frequency distribution of observations, measured by mean, median and mode

measures of spread

• describe how similar or varied the set of observed values are for a particular variable

• range, quartiles and the interquartile range, variance and standard deviation

parametric tests

• a family of statistical tests that require data to meet certain assumptions, in particular around the distribution of the data and the inter-relation between variable levels

• the basic assumptions: data are normally distributed, homogeneity of variance, interval or ratio data, the independence of scores

• for a correlational design there is also the assumption that the relationship between the variables will be linear

homogeneity of variance

an assumption for parametric testing in between-groups designs, where the variance of one variable is stable (roughly equal) at all levels of another variable

independent samples / between subjects t-test

a test using the t-statistic that establishes whether two means collected from independent samples differ significantly

repeated measures / within subjects t-test

a test using the t-statistic that establishes whether two means collected from the same sample differ significantly

non-parametric tests

• a family of statistical tests that don’t rely on the restrictive assumptions of parametric tests

• in particular they don’t assume sampling distribution is normal

• these tests are used when the data fails to meet the assumptions for a parametric test

correlation coefficient

• a measure of the strength and direction of the association between two variables

• there are two common variants - Pearson’s for parametric data, and Spearman’s for non-parametric data

• coefficients range between -1 and 1

• the closer the coefficient is to +/- 1, the stronger the relationship between the two variables

• coefficients close to 0 indicate that there’s little to no relationship between the variables being examined

Mann-Whitney test

• a non-parametric test which examines differences between two independent samples

• the non-parametric equivalent of an independent t-test

Wilcoxon’s signed-rank test

• a non-parametric test which examines differences between two independent samples

• the non-parametric equivalent of the related t-test

test statistic

• how frequently different values occur in random samples

• the observed value of such a statistic is usually used to test a hypothesis

• for a t-test, the test statistic is “t” and the value of t needs to be reported alongside the p-value in the presentation of results

p values

• p represents the likelihood of the data be due to chance

• in psychology, a critical p-value of 0.050 is used to test whether there’s a significant difference between two groups or conditions, or a significant relationship between two variables