Week 11 Lecture SWIN BUR NE SWINBURNE UNIVERSITY OF TECHNOLOGY STA10003 FOUNDATIONS OF STATISTICS Sandra Wyatt KNOW ING 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 · Report writing! 2 1
Revision of Week 10 0 0 Assignment Mark [out of 20) 0 0 0004 0 0 Number of Tutorials Attended (up to / including Week 7] r2 = 0.112 Correlations Assignment Mark [out of 20] Number of Tutorials Attended Pearson Correlation 1 .335 ** Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) Number of Tutorials Attended [up to / including Assignment Mark [out of 20] Week 7] .000 312 312 .335 ** 1 .000 [up to / including Week 7] N 312 312 **. Correlation is significant at the 0.01 level (2-tailed). 95% Confidence Interval: (0.23, 0.43) Model 1 (Constant) Coefficientsª Standardiz ed Coefficient s Unstandardized Coefficients Std. Error Beta B 8.884 .661 t 13.439 Number of Tutorials Attended [up to / including Week 7] .723 .116 .335 6.253 .000 95.0% Confidence Interval for B Lower Bound 7.583 Upper Bound 10.185 Sig. .000 .496 .951 a. Dependent Variable: Assignment Mark [out of 20] Note: This information relates to a previous cohort of STA10003 students IING 3 Report Writing It was hypothesised that STA10003 statistics students who attend more tutorials tend to achieve higher marks for the Assignment. In this cohort of STA10003 students [who submitted an Assignment], there was a moderate strength, positive, linear relationship between Assignment marks achieved and the number of tutorials attended, and Pearson's r shows that this relationship is significant (r = . 34, n = 312, p < . 001). The 95% confidence interval for Pearson's r indicates that the strength of the relationship is between p = . 23 and p = . 43. For each additional tutorial attended, on average, Assignment marks were 0.72 higher / more. Conclusion? 0 r2 interpretation: 11.2% of the variation is Assignment marks can be explained by the linear relationship between tutorial attendance and Assignment marks. 4 2
Overview . Parametric and Non-Parametric Tests · Crosstabulations and Chi-Square [12] · Chi-Square Test for Goodness of Fit • For information purposes / background · Chi-Square Test for Independence · Report writing · Putting together our crosstabulations and Chi-Square information - What to report ... · Risk / Odd Ratios KNOW ING 5 Parametric and Non-Parametric Tests · Parametric Tests · Numerical scores · Assumptions about population parameters · eg population means / mean difference · normality of population distributions · Non-Parametric Tests · Categories or groups