Practice A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. Determine if age is related to life satisfaction.

Older AdultsYounger Adults

OlderYounger Mean = 44.5Mean = 28.1 S = S = S 2 = S 2 = t obs = 4.257; t crit = Age is related to life satisfaction.

What if.... The two samples have different sample sizes (n)

Results Psychology Sociology

Results Psychology Sociology

If samples have unequal n All the steps are the same! Only difference is in calculating the Standard Error of a Difference

Standard Error of a Difference When the N of both samples is equal If N 1 = N 2 : Sx 1 - x 2 =

Standard Error of a Difference When the N of both samples is not equal If N 1 = N 2 : N 1 + N 2 - 2

Results Psychology Sociology  X 1 = 535  X 1 2 = N 1 = 4  X 2 = 265  X 2 2 = N 2 = 3

N 1 + N  X 1 = 535  X 1 2 = N 1 = 4  X 2 = 265  X 2 2 = N 2 = 3

N 1 + N  X 1 = 535  X 1 2 = N 1 = 4  X 2 = 265  X 2 2 = N 2 =

N 1 + N  X 1 = 535  X 1 2 = N 1 = 4  X 2 = 265  X 2 2 = N 2 =

 X 1 = 535  X 1 2 = N 1 = 4  X 2 = 265  X 2 2 = N 2 =

5  X 1 = 535  X 1 2 = N 1 = 4  X 2 = 265  X 2 2 = N 2 =

5  X 1 = 535  X 1 2 = N 1 = 4  X 2 = 265  X 2 2 = N 2 = (.58)

5  X 1 = 535  X 1 2 = N 1 = 4  X 2 = 265  X 2 2 = N 2 = = 10.69

Practice I think it is colder in Philadelphia than in Anaheim (  =.10). To test this, I got temperatures from these two places on the Internet.

Results Philadelphia Anaheim

Hypotheses Alternative hypothesis –H 1 :  Philadelphia <  Anaheim Null hypothesis –H 0 :  Philadelphia = or >  Anaheim

Step 2: Calculate the Critical t df = N 1 + N df = = 6  =.10 One-tailed t critical =

Step 3: Draw Critical Region t crit = -1.44

Now Step 4: Calculate t observed t obs = (X 1 - X 2 ) / Sx 1 - x 2

6  X 1 = 275  X 1 2 = N 1 = 5 X 1 = 55  X 2 = 219  X 2 2 = N 2 = 3 X 2 = = 3.05

Step 4: Calculate t observed = ( ) / 3.05 Sx 1 - x 2 = 3.05 X 1 = 55 X 2 = 73

Step 5: See if t obs falls in the critical region t crit = t obs = -5.90

Step 6: Decision If t obs falls in the critical region: –Reject H 0, and accept H 1 If t obs does not fall in the critical region: –Fail to reject H 0

Step 7: Put answer into words We Reject H 0, and accept H 1 Philadelphia is significantly (  =.10) colder than Anaheim.

SPSS

So far.... We have been doing independent samples designs The observations in one group were not linked to the observations in the other group

Example Philadelphia Anaheim

Matched Samples Design This can happen with: –Natural pairs –Matched pairs –Repeated measures

Natural Pairs The pairing of two subjects occurs naturally (e.g., twins)

Matched Pairs When people are matched on some variable (e.g., age)

Repeated Measures The same participant is in both conditions

Matched Samples Design In this type of design you label one level of the variable X and the other Y There is a logical reason for paring the X value and the Y value

Matched Samples Design The logic and testing of this type of design is VERY similar to what you have already done!

Example You just invented a “magic math pill” that will increase test scores. On the day of the first test you give the pill to 4 subjects. When these same subjects take the second test they do not get a pill Did the pill increase their test scores?

Hypothesis One-tailed Alternative hypothesis –H 1 :  pill >  nopill –In other words, when the subjects got the pill they had higher math scores than when they did not get the pill Null hypothesis –H 0 :  pill < or =  nopill –In other words, when the subjects got the pill their math scores were lower or equal to the scores they got when they did not take the pill

Results Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) 1 3 2

Step 2: Calculate the Critical t N = Number of pairs df = N = 3  =.05 t critical = 2.353

Step 3: Draw Critical Region t crit = 2.353

Step 4: Calculate t observed t obs = (X - Y) / S D

Step 4: Calculate t observed t obs = (X - Y) / S D

Step 4: Calculate t observed t obs = (X - Y) / S D X = 3.75 Y = 2.00

Step 4: Calculate t observed t obs = (X - Y) / S D Standard error of a difference

Step 4: Calculate t observed t obs = (X - Y) / S D S D = S D / N N = number of pairs

S =

Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) 1 3 2

S = Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) Difference (D) 2 1

S = Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) Difference (D) 2 1  D = 7  D 2 =13 N = 4

S = Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) Difference (D) 2 1  D = 7  D 2 =13 N = 4 7

S = Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) Difference (D) 2 1  D = 7  D 2 =13 N =

S = Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) Difference (D) 2 1  D = 7  D 2 =13 N =

S = Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) Difference (D) 2 1  D = 7  D 2 =13 N =

.5 = Test 1 w/ Pill (X) Mel3 Alice5 Vera 4 Flo3 Test 2 w/o Pill (Y) Difference (D) 2 1  D = 7  D 2 =13 N =

Step 4: Calculate t observed t obs = (X - Y) / S D S D = S D / N N = number of pairs

Step 4: Calculate t observed t obs = (X - Y) / S D.25=.5 / 4 N = number of pairs

Step 4: Calculate t observed 7.0 = ( ) /.25

Step 5: See if t obs falls in the critical region t crit = 2.353

Step 5: See if t obs falls in the critical region t crit = t obs = 7.0

Step 6: Decision If t obs falls in the critical region: –Reject H 0, and accept H 1 If t obs does not fall in the critical region: –Fail to reject H 0

Step 7: Put answer into words Reject H 0, and accept H 1 When the subjects took the “magic pill” they received statistically (  =.05) higher math scores than when they did not get the pill

SPSS

Practice You just created a new program that is suppose to lower the number of aggressive behaviors a child performs. You watched 6 children on a playground and recorded their aggressive behaviors. You gave your program to them. You then watched the same children and recorded this aggressive behaviors again.

Practice Did your program significantly lower (  =.05) the number of aggressive behaviors a child performed?

Results Time 1 (X) Child118 Child211 Child319 Child46 Child510 Child614 Time 2 (Y)

Hypothesis One-tailed Alternative hypothesis –H 1 :  time1 >  time2 Null hypothesis –H 0 :  time1 < or =  time2

Step 2: Calculate the Critical t N = Number of pairs df = N = 5  =.05 t critical = 2.015

Step 4: Calculate t observed t obs = (X - Y) / S D

1.21 = (D)  D = 8  D 2 =18 N = Time 1 (X) Child118 Child211 Child319 Child46 Child510 Child614 Test 2 (Y)

Step 4: Calculate t observed t obs = (X - Y) / S D.49=1.21 / 6 N = number of pairs

Step 4: Calculate t observed 2.73 = ( ) /.49 X = 13 Y = S D =.49

Step 5: See if t obs falls in the critical region t crit = t obs = 2.73

Step 6: Decision If t obs falls in the critical region: –Reject H 0, and accept H 1 If t obs does not fall in the critical region: –Fail to reject H 0

Step 7: Put answer into words Reject H 0, and accept H 1 The program significantly (  =.05) lowered the number of aggressive behaviors a child performed.

SPSS

New Step Should add a new page Determine if –One-sample t-test –Two-sample t-test If it is a matched samples design If it is a independent samples with equal N If it is a independent samples with unequal N

Thus, there are 4 different kinds of designs Each design uses slightly different formulas You should probably make up ONE cook book page (with all 7 steps) for each type of design –Will help keep you from getting confused on a test

Practice Does drinking milkshakes affect (alpha =.05) your weight? To see if milkshakes affect a persons weight you collected data from 5 sets of twins. You randomly had one twin drink water and the other twin drank milkshakes. After 3 months you weighed them.

Results Water Twin A186 Twin B200 Twin C190 Twin D162 Twin E175 Milkshakes

Hypothesis Two-tailed Alternative hypothesis –H 1 :  water =  milkshake Null hypothesis –H 0 :  water =  milkshake

Step 2: Calculate the Critical t N = Number of pairs df = N = 4  =.05 t critical = 2.776

Step 3: Draw Critical Region t crit = 2.776t crit =

Step 4: Calculate t observed t obs = (X - Y) / S D

3.04 = (D)  D = -28  D 2 =194 N =

Step 4: Calculate t observed t obs = (X - Y) / S D 1.36=3.04 / 5 N = number of pairs

Step 4: Calculate t observed = (182.6 – 188.2) / 1.36 X = Y = S D = 1.36

Step 5: See if t obs falls in the critical region t crit = 2.776t crit = t obs = -4.11

Step 6: Decision If t obs falls in the critical region: –Reject H 0, and accept H 1 If t obs does not fall in the critical region: –Fail to reject H 0

Step 7: Put answer into words Reject H 0, and accept H 1 Milkshakes significantly (  =.05) affect a persons weight.

Practice Sleep researchers decide to test the impact of REM sleep deprivation on a computerized assembly line task. Subjects are required to participate in two nights of testing. On each night of testing the subject is allowed a total of four hours of sleep. However, on one of the nights, the subject is awakened immediately upon achieving REM sleep. Subjects then took a cognitive test which assessed errors in judgment. Did sleep deprivation lower the subjects cognitive ability?

REM DeprivedControl Condition

t obs = t crit = 1.83 Sleep deprivation lowered their cognitive abilities.