Quantitative Data Types and Tests

Reviewed and revised 26 August 2015

OVERVIEW

• quantitative data is that which can be expressed numerically and is associated with a measurement scale
• not all numbers constitute quantitative data (e.g. tax file number!)

DATA TYPES

• Interval data – increase at constant intervals but do not start at true zero (ie. gauge pressure or temperature on C scale – 20C is not twice as hot as 10C).
• Ratio data – a type of interval data but has a true zero (ie. absolute pressure of 200kPa is twice as great as 100kPa).
• Dichotomous or binary data – value of variable has only two alternatives (ie. yes or no)
• Discrete data – where data points are isolated and separated by gaps. (ie. number of cases of influenza)
• Continuous data – where data points are part of a continuous range of values (ie. height)

DESCRIPTIVE STATISTICS

• central tendency — mean, medain, and mode
• dispersion — range, inter-quartile range, deviation (distance between an observed score and the mean for the variable under consideration) and variance (deviation squared), standard deviation (square-root of variance)
• shape — skewness (positive or negative), kurtosis (peakedness)

INFERENTIAL STATISTICS

• used for hypothesis testing
• The null hypothesis (H0) is of the form there is no difference between these variables or groups or there is no association between these variables, one does not affect the value of the other
• The alternative hypothesis (H1) is that there is an association or difference

STATISTICAL TESTS

Use

• statistical tests are used to answer the question: “If the null hypothesis is true, how likely is it that I would observe the data that I have collected?” (usually expressed as a p-value)
• a two-tailed test is used to determine if the two vaules are different
• a one-tailed test is used to determine if one value is greater or smaller than the other

Types

• either parametric or non-parametric
• parametric methods makes assumptions about the distribution of data, non-parametric do not
• parametric methods are more powerful and should be used if possible, but require assumptions about the data to be met (e.g. normally distributed)

Parametric Tests

• Normal distribution (n > 60, mean, standard deviations, p value, alpha value, beta value)
• Students t Test (n < 60) – can be paired (same subjects on two different variables) or unpaired (independent samples); t statistic can only be computed for 2 groups or variables
• Analysis of variance (ANOVA): tests for differences between the means of 2 or more groups
• Pearson correlation co-efficient (Pearson’s R): tests for an association between two variables with an indication of strength
• Regression or multiple regression: tests if an independent variable can predict another variable(s)

Non-parametric tests

• Mann-Whitney U test: equivalent to unpaired Students t-test
• Wilcoxon rank sum test: equivalent to paired t-test
• Wilcox signed rank test: equivalent to paired t-test
• Kruskal-Wallis: equivalent to one-way ANOVA
• Friedman’s: equivalent to repeated measures ANOVA
• Spearman’s rank order (ρ): equivalent to Pearson correlation co-efficient but for ranked data