Class notes 3.28.17 PDF

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March 28, 2017 Paired T-Test and Chi Squared Test Means don’t matter if you trying to compare differences  paired test If you save the differences, run a one sample test with differences against 0 Average difference = 0, average difference =/ 0 Email Access Data - At 95% Confidence Level, what is t-critical? Df = 15-1 = 14 Table: 2.145 (two tail alpha = .05) T-Stat: -3.596 One tail (is one faster/slower) vs. two tail (is there a difference)? More interested in something being faster, a direction instead of just equal 95% confident that Email Access 1 is at least .16 and up to .64 seconds faster than Email Access 2 Hypothesis Testing Comparing sample results to some given # Hypothesis is about a proportion – one sample z test Hypothesis is about a mean – one sample t test Comparing two groups Hypothesis is about the mean of two independent groups – t test for independent groups Hypothesis is about the mean differences in two paired samples – paired t test Hypothesis is about comparing the distribution of categories of a categorical variable – chi squared test Chi-Squared Given all at once, does it reasonably fit what we expect to see Skewed distribution, but still a probability distribution Chi-Squared Test Statistic (Observed – expected)^2 / Expected for each category, add up Squared because we don’t care about direction, just distance Measures how far away are the observations from the expected as a percentage of the expected T-stat = 6.86 Then need a critical value Df = k -1 (k is number of cells), 6 -1 = 5 Test stat should be greater than critical value 95% confidence interval, Critical value = 11.070 Is 6.86 further away than 11.070? No  cannot reject StatCrunch Stat > Goodness of Fit > Chi square Expected Standardized residuals: biggest have the biggest differences

Chi-Squared v. one sample proportion test – Chi squared looks holistically, a group, (fundamentally matches or doesn’t match), one proportion looks at just one measure, stand alone Chi-Squared Test for Independence Hypothesis same for all tests of independence H0: Variables are independent HA: Variables are not independent Degrees of Freedom = (# rows -1) * (# columns – 1) If they’re independent, expected value should be probability of being female * probability of liking shopping  number out of total StatCrunch Stat > Tables > Contingency > Summary Columns: Male, Female Row labels: Likes Shopping Display: Standardized Chi-Squared Test residuals Hypothesis tests: Chi-Squared test for independence Two sample z test for proportions...