 What is t test  Types of t test  TTEST function  T-test ToolPak 2

 In most cases, the z-test requires more information than we have available  We do inferential statistics to learn about the unknown population but, ironically, we need to know characteristics of the population to make inferences about it  Enter the t-test: “estimate what you don’t know” 3

 Employed by Guinness Brewery, Dublin, Ireland, from 1899 to  Developed t-test around 1905, for dealing with small samples in brewing quality control.  Published in 1908 under pseudonym “Student” (“Student’s t-test”) 4

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 Degrees of freedom describes the number of scores in a sample that are free to vary.  degrees of freedom = df = n-1  The larger, the better 6

 Very similar like z test  Use sample statistics instead of population parameters (mean and standard deviation)  Evaluate the result through t test table instead of z test table 7

 We show 26 babies the two pictures at the same time (one with his/her mother, the other a scenery picture) for 60 seconds, and measure how long they look at the facial configuration.  Our null assumption is that they will not look at it for longer than half the time, μ = 30  Our alternate hypothesis is that they will look at the face stimulus longer and face recognition is hardwired in their brain, not learned (directional)  Our sample of n = 26 babies looks at the face stimulus for M = 35 seconds, s = 16 seconds  Test our hypotheses ( α =.05, one-tailed) 8

 Sentence:  Null: Babies look at the face stimulus for less than or equal to half the time  Alternate: Babies look at the face stimulus for more than half the time  Code Symbols: 9

 Population variance is not known, so use sample variance to estimate  n = 26 babies; df = n-1 = 25  Look up values for t at the limits of the critical region from our critical values of t table  Set α =.05; one-tailed  tcrit =

 Central Limit Theorem  μ = 30  s M =s/ =16/ = 3.14  11

 The tobt=1.59 does not exceed tcrit=1.708  ∴ We must retain the null hypothesis  Conclusion: Babies do not look at the face stimulus more often than chance, t(25) = +1.59, n.s., one-tailed. Our results do not support the hypothesis that face processing is innate. 12

 A research design that uses a separate sample for each treatment condition is called an independent-measures (or between-subjects) research design. 13

 The goal of an independent-measures research study:  To evaluate the difference of the means between two populations.  Mean of first population: μ 1  Mean of second population: μ 2  Difference between the means: μ 1- μ 2 14

 Null hypothesis: “no change = no effect = no difference”  H0: μ 1- μ 2 = 0  Alternative hypothesis: “there is a difference”  H1: μ 1- μ 2 ≠ 0 15

Value for degrees of freedom: df = df1 + df2 16

Group 1 Group

 Step 1: A statement of the null and research hypotheses.  Null hypothesis: there is no difference between two groups  Research hypothesis: there is a difference between the two groups 18

 Step 2: setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis 

 Step 3: Selection of the appropriate test statistic  Determine which test statistic is good for your research  Independent t test 20

 Step 4: computation of the test statistic value  t=

 Step 5: determination of the value needed for the rejection of the null hypothesis  T Distribution Critical Values Table 22

 Step 5: (cont.)  Degrees of freedom (df): approximates the sample size  Group 1 sample size -1 + group 2 sample size -1  Our test df = 58  Two-tailed or one-tailed  Directed research hypothesis  one-tailed  Non-directed research hypothesis  two-tailed 23

 Step 6: A comparison of the obtained value and the critical value  0.14 and  If the obtained value > the critical value, reject the null hypothesis  If the obtained value < the critical value, retain the null hypothesis 24

 Step 7 and 8: make a decision  What is your decision and why? 25

 How to interpret t (58) = 0.14, p>0.05, n.s. 26

 T.TEST (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 two-sample test with unequal variances 27

 It does not compute the t value  It returns the likelihood that the resulting t value is due to chance (the possibility of the difference of two groups is due to chance) 28

 Select t-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Equal Variances Variable 1Variable 2 Mean Variance Observations30 Pooled Variance Hypothesized Mean Difference0 df58 t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail

 If two groups are different, how to measure the difference among them  Effect size ES: effect size : the mean for Group 1 : the mean for Group 2 SD: the standard deviation from either group 30

 A small effect size ranges from 0.0 ~ 0.2  Both groups tend to be very similar and overlap a lot  A medium effect size ranges from 0.2 ~ 0.5  The two groups are different  A large effect size is any value above 0.50  The two groups are quite different  ES=0  the two groups have no difference and overlap entirely  ES=1  the two groups overlap about 45% 31