W9 non-parametric approaches

Question 1

Parametric v non-parametric approaches

Answer 1

• parametric tests also make assumptions about the distribution of the population from which the data were randomly sampled
• all the tests we’ve looked at so far have all assumed that the data is normally distributed
• > e.g., t-test assumes that the sampling error is distributed normally around m
• non-parametric tests do not make a priori assumptions about the specific shape of the distribution—hence they’re also known as distribution-free tests

Question 2

Advantages of non-parametric tests

Answer 2

• they do not require assumptions of normality and homogeneity of variances (severely skewed data can be analysed with nonparametric statistics)
• ideal for analysing data from small samples (small samples are often skewed and can’t be rescued by the central limit theorem)
• generally easier to calculate–require less computation
• use of ranks reduces effect of extreme outliers

Question 3

Ranking in non-parametric approaches

Answer 3

• ranking merely involves the ordering of a set of scores from the smallest to the largest
• the smallest is given the rank of 1, the second smallest is 2, the 50th is 50
• provides a standard distribution of scores with standard characteristics

Question 4

Spearman’s Rho

Answer 4

• Spearman’s rho (rS) is calculated using Pearson’s r formula - the difference is that the data is ranked
• it can be used when you have two continuous variables, but one (or both) is badly skewed due to extreme scores

this is handy if:

• the data naturally falls in ranks
• there are extreme scores in your sample
• there is a monotonic relationship between the variables

Question 5

The null hypothesis

Answer 5

• the goal of any non-parametric test is to establish overall differences between two (or possibly more) distributions, not to identify the differences between any particular parameters
• as a result, H0 is more general
• > samples come from identical populations, not just populations with the same mean
• > rejecting H0 means that populations differ (perhaps not just on the basis of their central tendency - i.e., the mean)

Question 6

Point biserial correlation

Answer 6

• Pearson’s r is appropriate for describing linear relationships between two continuous variables
• if one variable is genuinely dichotomous, score one level of that variable as 0 and the other as 1 (or 1 and 2, or any two numbers)
• > compute correlation using Pearson’s r formula
• > referred to as the point-biserial correlation (rpb)

Question 7

interpretation of point biserial correlation

Answer 7

• absolute value of rpb reflects strength of the relationship
• but the sign of the correlation depend on scoring (0 or 1; or 1 and 2)
• r2pb interpreted the same way as r2
• test for significance in same way as for Pearson’s r

Question 8

rPB and t test

Answer 8

• alternatively we could examine the relationship between a dichotomous and a continuous variable using an independent groups t-test
• result of test of significance of rPB and t-test will be identical