KIN 4310 1st Edition Lecture 14Outline of Last Lecture I. Decision Criterion: another optionII. Non-Directional or Two-tailed TestIII. Directional Right-tailed TestIV. Directional Left-tailed TestV. Type 1 ErrorVI. Type 2 ErrorVII. Type 1 and Type 2 ErrorsVIII. Controlling Type 1 and Type 2 ErrorsIX. Fish Oil StudyX. HypothesesXI. Hypothesis TestsXII. One-sample Z TestXIII. One-sample Z Test ExampleXIV. One-sample Z Test cont.XV. ExampleOutline of Current Lecture I. ExampleII. Excel: Normal DistributionThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.III. The t-testIV. The t-test StepsV. Example: Reaction Time StudyVI. The t-testVII. The t-test InformationVIII. QuestionIX. Fish Oil StudyX. The t-test Excel FunctionsCurrent LectureI. Examplea. Conclusion: The residents of Grand Isle have higher mercury levels than the general populationi. So we reject the null hypothesis. The Grand Isle people have a significantly different level than the population.b. What is the p-value?i. The area in both of the tailsc. Table B1:i. The area between the mean and z = 2.16 is 48.16%, therefore, p-value is 0.0308.II. Excel: Normal Distributiona. =NORMDIST(x, mean, standard_dev, cumulative)i. Finds area under the curve to the left of a given valueii. Works for raw x scores or z-scoresiii. Always set cumulative to TRUEiv. Example:1. =NORMDIST(2.16, 0, 1, TRUE)a. Gives the area under the curve left of z = 2.162. =NORMDIST(-2.16, 0, 1, TRUE)a. Gives the area under the curve left of z = -2.16b. =NORMINV(probability, mean, standard_Dev)i. Finds the value that has a given proportion of the area under the curve tothe left of itii. Useful for finding critical valuesiii. Example1. =NORMINV(0.95, 0, 1)a. Gives the critical value of z for a right-tailed testIII. The t-testa. A special hypothesis test that is used to determine if there is a significant difference between two groupsb. E.g., when your research hypothesis is:i.c. Note: whenever you have two groups and want to know if there is a significant difference between the twod. Like all hypothesis tests, a t-test will tell you whether or not you should reject thenull hypothesise. In other words, are your results statistically significant?f. AKA Student’s test = the independent t-testg. You need the following:i.IV. The t-test Stepsa. Step 1: calculate the t-valuei. Equation:ii.b. Step 2: After you know the t-value, you must determine the degrees of freedom (df)i. df = n1 + n2 – 2ii. Degrees of freedom affect the shape of the t-distributionc. The t-distribution looks similar to the standard normal distributiond. It is symmetricale. Mean: t = 0f. Step 3: Determine the critical value of ti. Remember: the critical value is the cutoff value of the test statistic that will cause us to reject HOii. Use table B2 on page 370 of your textbookg. Step 4: Compare your t-value to the critical valuei. Make a decision1. Reject HO2. Don’t reject HOV. Example: Reaction Time Studya. H1: People who consider themselves fast have different RT than those who consider themselves slowb. 95 subjectsc. Self assign to: fast group and slow groupd. FASTi.e. SLOWf.g. t = -1.25h. df = 93VI. The t-testa. Critical valuei. Is this a one-tailed or two tailed test?ii. What is our significance level?b. For a two-tailed test with df = 95, alpha = 0.05i. Critical value is -1.986 and +1.986c. Decisioni. Our t-value is -1.25ii. Our critical value is -1.986d. So..i. We fail to reject the null hypothesisii. The reaction time of people who consider themselves fast is not significantly different than people who consider themselves slowVII. The t-test Informationa. Student’s t-test is used to determine if there is a significant difference between two groupsb. It is a quick and easy test that is applicable in many studiesVIII. Questiona. Table B2 gives us:i. The area between the mean and the t-valueii. The cumulative frequency of the t-distributioniii. The difference between two groupsiv. Critical values of the t-statisticv. A headacheIX. Fish Oil Studya.b. t = 3.06c. df = 12d. Critical value of t, based on a two-tailed test for df = 12, alpha = 0.05i. tcrit = +/- 2.179e. Since 3.06 > 2.179, we should reject HOX. The t-test Excel Functionsa. Performing t-tests in Excelb. Functionsi. TTEST1. TTEST(array1, array2, tails, type)a. Returns the p-valueb. Does the whole t-test without even telling you what t isc. Array1 is the first group’s datad. Array2 is the second group’s datae. Tails is the number of tails (1 or 2)f. Type is the type of t-testi. 1 = t-test for dependent meansii. 2 = t-test for independent means (equal variance)iii. 3 = t-test for independent means (unequal variance)ii. TDIST1. TDIST(t, deg_freedom, tails)a. Returns the area in the tail(s) beyond t2. Examplea. TDIST(1.5, 17, 2) gives the area in the tails for t < -1.5 and t > 1.53. If you know the t-score, you can use thisiii. TINV1. TINV(alpha, deg_freedom)a. Returns the critical t-score for a givenb. Only works for two-tailed tests2. Examplea. TINV(0.05, 17) = 2.11i. Returns the critical t-score for a two-tailed t-test with 17 degrees of freedom and alpha =