3003PSY Survey Design and Analysis in Psychology PDF

3003PSY Survey Design and Analysis in Psychology NON-PARAMETRIC TESTS: SPEARMAN'S RHO  uAll of the tests we have considered up to this point have involved: PARAMETRIC VS. uestimating population parameters NON- PARAMETRIC uassumptions about the sha...

3003PSY Survey Design and Analysis in Psychology NON-PARAMETRIC TESTS: SPEARMAN'S RHO  uAll of the tests we have considered up to this point have involved: PARAMETRIC VS. uestimating population parameters NON- PARAMETRIC uassumptions about the shape of the data TESTS uassumptions about the scaling of the variables  uparametric tests involve the estimation of at least one population parameter ESTIMATING POPULATION ue.g., t-test uses sample variance PARAMETERS to estimate the population variance unon-parametric tests do not— hence the name ASSUMPTIONS ABOUT THE SHAPE OF THE DATA uparametric tests also make assumptions about the distribution of the population from which the data were randomly sampled uall the tests we’ve looked at so far have all assumed that the data is normally distributed ue.g., t-test assumes that the sampling error is distributed normally around m unon-parametric tests do not make a priori assumptions about the specific shape of the distribution—hence they’re also known as distribution-free tests ASSUMPTIONS ABOUT THE SCALING OF THE VARIABLE uParametric tests assume the outcome variable has been measured at interval or ratio level uNon-parametric tests do not  NON-PARAMETRIC TESTS: ADVANTAGES uthey do not require assumptions of normality and homogeneity of variances (severely skewed data can be analysed with nonparametric statistics) uideal for analysing data from small samples (small samples are often skewed and can’t be rescued by the central limit theorem) ugenerallyeasier to calculate--require less computation uuse of ranks reduces effect of extreme outliers EXPLAINING RANKING 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 the rank of 2 … the 50th the rank of 50 it provides a standard distribution of why rank? scores with standard characteristics  Normal Data 8 €€€€€ € 1.2 1.9 2.1 2.4 2.6 9.2 When Ranked €€ € € € € 1 2 3 4 5 6 SPEARMAN Pearson’s correlation coefficient r is based on RANK-ORDER assumptions: CORRELATION interval or ratio data, COEFFICIENT X and Y are normally distributed, and (OR a linear relationship between X and SPEARMAN’S Y RHO) So we assume a bivariate normal distribution based on interval or ratio scales SPEARMAN’S RHO u Spearman's rho (rS) is calculated using Pearson’s r formula - the difference is that the data is ranked u 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  100 90 80 Percent Conforming 70 60 A MONOTONIC 50 40 RELATIONSHIP 30 20 10 0 0 1 2 3 5 6 7 8 Size of Crowd  9 8 7 Conformity Rank 6 5 SPEARMAN’S 4 RHO 3 2 1 0 0 1 2 3 5 6 7 8 Size of Crowd  SPEARMAN’S RHO uanotherbenefit of Spearman’s rho is that it can be used when you have two continuous variables, but one (or both) is badly skewed due to extreme scores Scores: 10 1 1 12 13 14 176 Receive ranks of: 1 2 3 4 5 6 NONPAR CORR /VARIABLES=Stats_Exam GRE_Q /PRINT=SPEARMAN TWOTAIL NOSIG /MISSING=PAIRWISE.  u 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 THE NULL u as a result, H0 is more general HYPOTHESIS u samples come from identical populations, not just populations with the same mean u rejecting H0 means that populations differ (perhaps not just on the basis of their central tendency - i.e., the mean)  SUMMARY u Parametric tests involve estimating population parameters, making assumptions about the shape of the data and assumptions about the scaling of the variables u Non-parametric tests do not u Ranking is one approach used by non-parametric tests u Spearman's rho can be used to calculate correlations between variables that has natural ranks, there are extreme scores in your sample or there is a monotonic relationship between the variables uWhile fewer assumptions are required to be met non-parametric tests are generally less powerful than parametric tests.