KIN 4310 1st Edition Lecture 14 Outline of Last Lecture I Decision Criterion another option II Non Directional or Two tailed Test III Directional Right tailed Test IV Directional Left tailed Test V Type 1 Error VI Type 2 Error VII Type 1 and Type 2 Errors VIII Controlling Type 1 and Type 2 Errors IX Fish Oil Study X Hypotheses XI Hypothesis Tests XII One sample Z Test XIII One sample Z Test Example XIV One sample Z Test cont XV Example Outline of Current Lecture I Example II Excel Normal Distribution These 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 test IV The t test Steps V Example Reaction Time Study VI The t test VII The t test Information VIII Question IX Fish Oil Study X The t test Excel Functions Current Lecture I Example a Conclusion The residents of Grand Isle have higher mercury levels than the general population i 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 tails c Table B1 i The area between the mean and z 2 16 is 48 16 therefore p value is 0 0308 II Excel Normal Distribution a NORMDIST x mean standard dev cumulative i Finds area under the curve to the left of a given value ii Works for raw x scores or z scores iii Always set cumulative to TRUE iv Example 1 NORMDIST 2 16 0 1 TRUE a Gives the area under the curve left of z 2 16 2 NORMDIST 2 16 0 1 TRUE a Gives the area under the curve left of z 2 16 b NORMINV probability mean standard Dev i Finds the value that has a given proportion of the area under the curve to the left of it ii Useful for finding critical values iii Example 1 NORMINV 0 95 0 1 a Gives the critical value of z for a right tailed test III The t test a A special hypothesis test that is used to determine if there is a significant difference between two groups b E g when your research hypothesis is c d e f g i Note whenever you have two groups and want to know if there is a significant difference between the two Like all hypothesis tests a t test will tell you whether or not you should reject the null hypothesis In other words are your results statistically significant AKA Student s test the independent t test You need the following i IV The t test Steps a Step 1 calculate the t value i Equation b c d e f ii Step 2 After you know the t value you must determine the degrees of freedom df i df n1 n2 2 ii Degrees of freedom affect the shape of the t distribution The t distribution looks similar to the standard normal distribution It is symmetrical Mean t 0 Step 3 Determine the critical value of t i Remember the critical value is the cutoff value of the test statistic that will cause us to reject HO ii Use table B2 on page 370 of your textbook g Step 4 Compare your t value to the critical value i Make a decision 1 Reject HO 2 Don t reject HO V Example Reaction Time Study a H1 People who consider themselves fast have different RT than those who consider themselves slow b 95 subjects c Self assign to fast group and slow group d FAST i e SLOW f g t 1 25 h df 93 VI The t test a Critical value i 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 05 i Critical value is 1 986 and 1 986 c Decision i Our t value is 1 25 ii Our critical value is 1 986 d So i We fail to reject the null hypothesis ii The reaction time of people who consider themselves fast is not significantly different than people who consider themselves slow VII The t test Information a Student s t test is used to determine if there is a significant difference between two groups b It is a quick and easy test that is applicable in many studies VIII Question a Table B2 gives us i The area between the mean and the t value ii iii iv v IX The cumulative frequency of the t distribution The difference between two groups Critical values of the t statistic A headache Fish Oil Study a b t 3 06 c df 12 d Critical value of t based on a two tailed test for df 12 alpha 0 05 i tcrit 2 179 e Since 3 06 2 179 we should reject HO X The t test Excel Functions a Performing t tests in Excel b Functions i TTEST 1 TTEST array1 array2 tails type a Returns the p value b Does the whole t test without even telling you what t is c Array1 is the first group s data d Array2 is the second group s data e Tails is the number of tails 1 or 2 f Type is the type of t test i 1 t test for dependent means ii 2 t test for independent means equal variance iii 3 t test for independent means unequal variance ii TDIST 1 TDIST t deg freedom tails a Returns the area in the tail s beyond t 2 Example a TDIST 1 5 17 2 gives the area in the tails for t 1 5 and t 1 5 3 If you know the t score you can use this iii TINV 1 TINV alpha deg freedom a Returns the critical t score for a given b Only works for two tailed tests 2 Example a TINV 0 05 17 2 11 i Returns the critical t score for a two tailed t test with 17 degrees of freedom and alpha 0 05