STA WEEK 11 Revision of week 10 · Exploring relationships between two metric variables · Scatterplots ... Check for linearity, sub-groups, outliers · Pearson's correlation co-efficient [Pearson's r ] · Used to measure the strength of the linear relationship · 95% Confidence Interval for Pearson's r [strength in population] · Co-efficient of determination [r 2] · Gives an indication of the 'importance' of the IV in predicting the DV · Regression Equation · Y = bX + a · Used to predict the value of the DV if we know something about the IV · Interpret regression coefficient [slope] · Rennrt writingl Parametric test - Numerical scores - Assumptions about populations parameters - Eg populations means / mean difference - Normality of population distributions Non - parametric tests - Categories or groups - Frequencies / % - No assumption about normality of distribution Why do we use non parametric test - Numerical scores may violate assumptions - Can use sample information - Could convert numerical info to categories / groups High level of variance in numerical data - Converting to categoties / groups eliminates variance - Either in this category or not Grouping is something's just more convenient
Chi- Square Statistic (X2) of independence Chi - square (X2) of independence · Test to determine of a relationship exists between two categorical variables · Based on sample information · Frequency distribution matrix (cross tabulation) · Relationship only - no causal conclusions can be made Null and alternative hypothesis H0: there is NO relationship between XXX and YYY H1: there IS a relationship between XXX and YYY Observed and expected frequencies - Same logic as goodness of fit - Same calculation for X2 EXAMPLE H0: there is no relationship between type of pet preferred and gender H1: there is a relationship between type of pet preferred and gender It is thought that males are more likely than females to prefer dogs as pets Can work out table, use basic maths Observed frequencies: Gender Males Females 20 Totals 50 Type of Pet Dog Cat / Other animal 70 100 30 30 50 100 150 Totals Degrees of Freedom calculated as (R - 1)(C - 1) df = (2 - 1)(2 - 1) df = 1 × 1 df = 1
Chi-square (X2) of independence Using column and row totals, we can calculate the expected frequencies and then calculate the X2 stats Male / Dog Preference fs = fcfr = 1 = 50 × 100 150 5000 2500 fs = 150 150 f= = 33.33 Female / Dog Preference = 50 × 50 150 fc =16.67 f = 33 fs = 17 Observed frequencies: Gender Type of Pet Dog Cat / Other animal Totals Gender Expected frequencies: Type of Pet Cat / Other Totals Dog animal Males 30 70 Females 20 Totals 50 100 30 50 100 150 Males 33 67 Females 17 33 Totals 50 100 50 100 150