May 10 2017

# GST1 – 6: Quantitative Methods in the Social Sciences 3

GST 1 is a module at Maynooth University which aims to improve research skills and employability. To gain 5 ECTS for this module you need to attend 6 sessions and produce a diary entry or set of notes for each one.

Quantitative Methods in the Social Sciences 3: Inferential and Exploratory Quantitative Techniques

Parametric and Non-Parametric Tests
The type of test chosen for your data depends on whether the data are parametric or non-parametric. Parametric data are:

• Independent randomly selected observations
• Approximately normally distributed
• Interval scale measurements – continuous
• Generally a minimum sample size of 30
• Hypothesis posed regarding mean, standard deviation of population

If the sample does not fit into the parametric criteria, or the data are ordinal or nominal. The hypothesis posed is regarding ranks, medians, frequencies or inter-quartile range. There are parallel statistical tests depending on your data.

 Parametric Non-Parametric Mean, Standard Deviation Chi Squared z-Test Kendall’s Tau Student’s t-Test Mann-Whitney U Test Pearson’s Product Moment Correlation Spearman’s Rank Correlation Coefficient

One of the biggest challenges is deciding which type of test to use:

• Difference between groups (independent) – t-test or Mann-Whitney U test
• Difference between dependent variables – t-test for dependent samples or Wilcoxon Sign-rank
• Relationship between variables – Pearson correlation or Spearman Correlation / Chi Square.

The choice of test will depend on your objectives, the distribution, data type, number of samples, what you are trying to do, and, ideally, whether you have used the test before. The steps to testing the hypothesis are:

1. Identify the research question
2. State H0 and Ha
3. Decide the level of significance – 95% or < 0.05 p value
4. Identify whether you need a 1 or 2-tailed test
5. Compute the test statistic
6. If it is in the critical region – reject H0

Student’s t-Test
There are three types of t-test and all compare the means. A 1-sample t-test compares the sample mean to a known population, e.g. 1st year students compared to whole student body. An independent sample t-test compares 2 independent groups, e.g. male vs female income. A Paired (dependent) samples t-test compares repeated measures, e.g. before and after in a drug trial.

Analysis of Variance (ANOVA)
ANOVA is a continuation of the t-test if you are using 3 or more samples. Using a series of t-tests is likely to create a Type I error, using ANOVA reduces this chance. The ANOVA (f statistic) is calculated by dividing an estimate of the variability between groups by the variability within groups. 