Chapter 10 Independent Samples t-Test

NOTE: Homework for Ch 10

Is DUE ON FRIDAY !!

Independent Samples• Means and variability from two samples• Population means & variability are unknown• Many possible situations

– Experimental groups– “Natural” experiments– Self-Selected groups– Demographic groups

• GROUP MEMBERSHIP MUST BE UNRELATED (INDEPENDENT OF) THEDEPENDENT VARIABLE (MEANS)

Four Steps of Hypothesis Test

• Step 1: Define Null & Alternate Hyp.

• Step 2: Locate the Critical Region– Define a range of values of t that will lead to

rejecting the null hypothesis– IN SPSS: define the value of p (reported as

“sig”) that will lead to rejecting null hypothesis

– Reject H0 if |t| > Critical Value of t

– Reject H0 if p (or “sig”) < Alpha level

• Let’s DO Problem 20 on p. 285

Figure 10-1 (p. 248)Do the achievement scores for children taught by method A differ from the scores for children taught by method B? In statistical terms, are the two population means the same or different? Because neither of the two population means is known, it will be necessary to take two samples, one from each population. The first sample will provide information about the mean for the first population, and the second sample will provide information about the second population.

PREPARATION:Gather all the information in anorderly way.

STEP ONE: State null and alternate Hypotheses as equations.

Figure 8-7 (p. 195)Sample means that fall in the critical region (shaded areas) have a probability less than alpha ( < ). H0 should be rejected. Sample means that do not fall in the critical region have a probability greater than alpha ( > ).

STEP TWO: LOCATE THE CRITICAL REGION

Determine α / Determine df / One-tailed or two-tailed?Find critical value in table, define rejection region on curve.

STEP 3: COLLECT THE DATA & COMPUTE• N(sleep)=• M(sleep)=• SS(sleep)=

• N(no sleep)=• M(no sleep)=• SS(no sleep)=

Pooled variance =

Estimated Std. Error =

t =

Table 10-1 (p. 253)The basic elements of a t statistic for the single-sample t and the independent-measures t.

Sample Pooled variance =

Table 10-1 (p. 253)The basic elements of a t statistic for the single-sample t and the independent-measures t.

Estimated Std. Error =

Table 10-1 (p. 253)The basic elements of a t statistic for the single-sample t and the independent-measures t.

t =

STEP 4: Make a Decision

Step 5: Write up the resultsSee posts on blog for detailed information.

Researchers thought that retention of newly learned skills might be affected by sleep after learning. After learning a new task, half of the subjects slept at least six hours and the others were kept awake all night. Participants who slept at least 6 hours scored significantly higher (M = 72, SD = 7.93) than those who stayed awake all night (M = 61, SD = 8.07) on a visual discrimination task learned the previous day (t(14) = 2.75, p < .05). More than a third of the variability in performance in the task is related to sleep level (r2 = .3510), Getting at least 6 hours of sleep had an important impact on performance of a recently learned task the following day.

Look at Problem 23 (p.286) in SPSS

1. Define two variables

2. One dividing the data into two groups(OwnDog in this example)

3. One for the dependent variable(DocVisits in this example)

4. Make Value Labels for grouping variable

5. Type in values of grouping variable first

6. Add values for dependent variable

Look at a box plot to visualize data

Compare medians, IQR, overlap

t-Test: Analyze→Compare Means → Independent Samples t-Test

A dialog box opens up …

Move Dependent variable into “Test Variable”

Move Grouping variable into “Grouping Variable” click “Define Groups”→Type in valuesclick “Continue” then “OK”

Descriptive statistics for each group:

• Mean No Dog = 11.14• SD No Dog = 3.078• N No Dog = 7

• Mean Owns Dog = 6.40• SD Owns Dog = 2.074• N Owns Dog = 5

Group Statistics

7 11.14 3.078 1.164

5 6.40 2.074 .927

OwnDog Dog Ownership0 No Dog

1 Owns Dog

DocVisits Number ofVisits to the Doctor inthe Last Year

N Mean Std. DeviationStd. Error

Mean

t-Test output is very wide

Independent Samples Test

.799 .392 2.976 10 .014 4.743 1.593 1.192 8.293

3.188 9.994 .010 4.743 1.488 1.427 8.058

Equal variancesassumed

Equal variancesnot assumed

DocVisits Number ofVisits to the Doctor inthe Last Year

F Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

What if the variances of the two groups are not equal? See Section 10.4

Use the top line of values unless the assumption has been violated.

Find value of t, df, the exact p-value (under “Sig.”) for write-up.

APA format: t(10) = 2.976, p = .014

Reject H0 if p-value is less than the selected α, which is usually .05.

Compute Cohen’s d or r2 by hand.

Write UpAre elderly people who own dogs healthier? Researchers compared the number of times elderly dog owners visited the doctor in the last year with the number of visits made by a similar group of people who do not own dogs. The dog owners averaged fewer visits (M = 6.40, SD = 2.074) than the others (M = 11.14, SD = 3.078). The difference was significant (t(10) = 2.976, p = .014) with dog ownership accounting for almost half of the variability in number of doctor visits (r2 = .4697). While the research does not demonstrate that the elderly dog owners actually have better health, it does show that they do make fewer visits to see the doctor.