advertisement

S519 Statistical Sessions Wrap up Things we’ve covered • • • • • • • • • Descriptive Statistics Normal Distributions Z-test Hypothesis Testing T-test ANOVA Correlation Linear regression Chi-square Descriptive Statistics • Central Tendency – Mean – Median – Mode • Variance – Range – Standard deviation – Variance Normal Distributions • Skewness • Kurtosis Z-test Hypothesis Testing 1. State the hypothesis – Null hypothesis – Research hypothesis • • Directional Non-directional 2. Set decision criteria 3. Collect data and compute sample statistic 4. Make a decision (accept/reject) T-test T-test • Degree of freedom=n-1 • TTEST (array1, array2, tails, type) – array1 = the cell address for the first set of data – array2 = the cell address for the second set of data – tails: 1 = one-tailed, 2 = two-tailed – type: 1 = a paired t test; 2 = a two-sample test (independent with equal variances); 3 = a twosample test with unequal variances ANOVA • Analysis of Variance • A hypothesis-testing procedure used to evaluate mean differences between two or more treatments (or populations). • Advantages: – 1) Can work with more than two samples. – 2) Can work with more than one independent variable ANOVA • In ANOVA an independent or quasiindependent variable is called a factor. • Factor = independent (or quasi-independent) variable. • Levels = number of values used for the independent variable. • One factor → “single-factor design” • More than one factor → “factorial design” ANOVA • Df for independent ANOVA – Between-group degree of freedom=k-1 • k: number of groups – Within-group degree of freedom=N-k • N: total sample size • Df for dependent ANOVA – Between-group degree of freedom=k-1 • k: number of groups – Within-group degree of freedom=N-k • N: total sample size – Between-subject degree of freedom=n-1 • n: number of subjects – Error degree of freedom=(N-k)-(n-1) ANOVA • Three different ANOVA: – Independent measures design: Groups are samples of independent measurements (different people) ANOVA: single factor – Dependent measures design: Groups are samples of dependent measurements (usually same people at different times) “Repeated measures” ANOVA: two factors without replication – Factorial ANOVA (more than one factor) ANOVA: two factors with replication Correlation • Pearson correlation – CORREL function or Pearson function – Toolpak for more than two variables (matrix) • The correlation represents the association between two or more variables • It has nothing to do with causality (there is no cause relation between two correlated variables) Correlation rxy value Interpretation 0.8 ~ 1.0 Very strong relationship (share most of the things in common) 0.6 ~0.8 Strong relationship (share many things in common) 0.4 ~ 0.6 Moderate relationship (share something in common) 0.2 ~ 0.4 Weak relationship (share a little in common) 0.0 ~ 0.2 Weak or no relationship (share very little or nothing in common) Correlation Linear regression • Y’ = bX + a – b = SLOPE() – a = INTERCEPT() • Chi-square • Non-parametric vs. parametric • 2 ( O E ) 2 E – O: the observed frequency – E: the expected frequency • df=r-1 (r= number of categories)