# T-test for dependent Samples. Difference Scores. The t Test for Dependent Samples. The t Test for Dependent Samples. s D

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1 The t Tet for ependent Sample T-tet for dependent Sample (ak.a., Paired ample t-tet, Correlated Group eign, Within- Subject eign, Repeated Meaure,.. Repeated-Meaure eign When you have two et of core from the ame peron in your ample, you have a repeated-meaure, or within-ubject deign. You are more imilar to yourelf than you are to other people. ifference Score The way to handle two core per peron, or a matched pair, i to make difference core. For each peron, or each pair, you ubtract one core from the other. Once you have a difference core for each peron, or pair, in the tudy, you treat the tudy a if there were a ingle ample of core (core that in thi ituation happen to be difference core. A Population of ifference Score with a Mean of 0 The null othei in a repeatedmeaure deign i that on the average there i no difference between the two group of core. Thi i the ame a aying that the mean of the ampling ditribution of difference core i 0. The t Tet for ependent Sample You do a t tet for dependent ample the ame way you do a t tet for a ingle ample, except that: You ue difference core. You aume the population mean i 0. The t Tet for ependent Sample μ n μ μ nσ ( Σ n( n

2 The t Tet for ependent Sample: Hypothei Teting. State the reearch quetion.. State the tatitical othei. 3. Set deciion rule. 4. Calculate the tet tatitic. 5. ecide if reult i ignificant. 6. Interpret reult a it relate to your reearch quetion. The t Tet for ependent Sample: State the reearch othei. oe litening to a pro-ocialized medicine lecture change an individual attitude toward ocialized medicine? State the tatitical othee. The t Tet for ependent Sample: Set the deciion rule. α.05 df number of difference core 8 7 t crit ±.365 H H O A : μ 0 : μ 0 The t Tet for ependent Sample: Calculate the tet tatitic. 6 8 nσ ( Σ n( n 8(4 ( 6. 8(7..4 n The t Tet for ependent Sample: ecide if your reult are ignificant. Reject H0, -4.76<-.365 Interpret your reult. After the pro-ocialized medicine lecture, individual attitude toward ocialized medicine were ignificantly more poitive than before the lecture.

3 Iue with Repeated Meaure eign Order effect. Ue counterbalancing in order to eliminate any potential bia in favor of one condition becaue mot ubject happen to experience it firt (order effect. Randomly aign half of the ubject to experience the two condition in a particular order. Practice effect. o not repeat meaurement if effect linger. Independent Sample The t Tet for Independent Sample Obervation in each ample are independent (not from the ame population of each other. We want to compare difference between ample mean. ( ( μ μ Sampling itribution of the ifference Between Mean Imagine two ampling ditribution of the mean... And then ubtracting one from the other If you create a ampling ditribution of the difference between the mean Given the null othei, we expect the mean of the ampling ditribution of difference, μ- μ, to be 0. We mut etimate the tandard deviation of the ampling ditribution of the difference between mean. Pooled Etimate of the Population Variance Uing the aumption of homogeneity of variance, both and are etimate of the ame population variance. If thi i o, rather than make two eparate etimate, each baed on ome mall ample, it i preferable to combine the information from both ample and make a ingle pooled etimate of the population variance. p (n + (n (n + (n Pooled Etimate of the Population Variance The pooled etimate of the population variance become the average of both ample variance, once adjuted for their degree of freedom. Multiplying each ample variance by it degree of freedom enure that the contribution of each ample variance i proportionate to it degree of freedom. You know you have made a mitake in calculating the pooled etimate of the variance if it doe not come out between the two etimate. You have alo made a mitake if it doe not come out cloer to the etimate from the larger ample. The degree of freedom for the pooled etimate of the variance equal the um of the two ample ize minu two, or (n- +(n-. 3

4 Etimating Standard Error of the ifference Between Mean p (n + (n (n + (n The t Tet for Independent Sample: Stereotype Threat p p + n n ( ( μ μ Trying to develop the tet itelf. Thi tet i a meaure of your academic ability. The t Tet for Independent Sample: State the reearch quetion. oe tereotype threat hinder the performance of thoe individual to which it i applied? State the tatitical othee. The t Tet for Independent Sample: Set the deciion rule. α.05 df ( n + ( n ( + ( t crit.7 H : μ μ 0 H : μ μ < 0 or o H : μ μ o H : μ < μ The t Tet for Independent Sample: Calculate the tet tatitic. The t Tet for Independent Sample: Calculate the tet tatitic. Control Control Sq Threat Threat Sq ( μ μ ( (6 (79 ( ( (06 (0 p (n + (n (n + (n p ( ( ( + ( p p + n n

5 The t Tet for Independent Sample: Calculate the tet tatitic. ( ( μ μ The t Tet for Independent Sample: ecide if your reult i ignificant. Reject H0, -.37< -.7 Interpret your reult. Stereotype threat ignificantly reduced performance of thoe to whom it wa applied. x Aumption The obervation within each ample mut be independent. The two population from which the ample are elected mut be normal. 3 The two population from which the ample are elected mut have equal variance. Thi i alo known a homogeneity of variance, and there are two method for teting that we have equal variance: a informal method imply compare ample variance b Levene tet We ll ee thi on the SPSS output 4 Random Aignment To make caual claim 5 Random Sampling To make generalization to the target population Which tet? Each of the following tudie require a t tet for one or more population mean. Specify whether the appropriate t tet i for one ample or two independent ample. College tudent are randomly aigned to undergo either behavioral therapy or Getalt therapy. After 0 therapeutic eion, each tudent earn a core on a mental health quetionnaire. One hundred college frehmen are randomly aigned to ophomore roommate having either imilar or diimilar vocational goal. At the end of their frehman year, the GPA of thee 00 frehmen are to be analyzed on the bai of the previou ditinction. According to the U.S. epartment of Health and Human Service, the average 6-year-old male can do 3 puh-up. A phyical education intructor find that in hi chool ditrict, 30 randomly elected 6-yearold male can do an average of 8 puh-up. For next week Read Ru Lenth paper on effective ample-ize determination. 5

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