PSY201: Chapter 10 - Independent Measures

Question 1

Confidence Intervals revisited

Answer 1

Therangeofscoreslikelytoincludethetruepopulationmean n Tells us how confident we are in our findings (based on the
chosen alpha level)
q e.g.,we’re95%confidentoursamplemeanfallsbetweena range of values
M +/- (t critical)(SM)

Question 2

Confidence Intervals: when useful

Answer 2

n t critical = 2.16

n Whatifift(13)=2.18?

Question 3

Independent-Measures Designs

Answer 3

The independent-measures hypothesis test (or between-subjects design) expands the single-sample t test to test for differences between two
separate groups
n Compares differences in the distribution between means

Question 4

Independent-Measures Designs

Answer 4

q One from one population, the other from a second population
n Allows researchers to evaluate the mean difference between two
populations using the data from two separate samples.

Question 5

Independent-Measures Designs

Answer 5

n Can be used to test for mean differences between two distinct populations (e.g., men vs. women) or between one sample given two different treatment conditions (e.g., drug vs. no-drug).

Question 6

Independent-Measures Design examples

Answer 6

A Social psychologist in interested in developmental trends in aggression. She compares the type and amount of aggressive behaviour in a group of 11 year old girls to those in a group of 11 year old boys (n = 50 in each group).
n Do Canadian young adults have different opinions about ethnic diversity than Canadian older adults?
n What is the effect of 0 mg vs 10 mg of a particular drug on reducing seizures in rats?

Question 7

Independent-Measures Design examples

Answer 7

Which is more effective, cognitive behaviour therapy (CBT) or drug therapy for treating depression in young teenagers?
In these cases, we may not know anything about the parent population distributions, except that if our samples are representative, the parent populations probably look a lot like our samples, and vice versa

Question 8

Independent-Measures Designs

Answer 8

The independent-measures design is used in situations where a researcher has no prior knowledge about either of the two populations (or treatments) being compared.
n In particular, the population means and standard deviations are all unknown.

Question 9

Independent-Measures Designs

Answer 9

Because the population variances are not known, these values must be estimated from the sample data.

Question 10

Hypothesis Testing with the Independent- Measures t Statistic

Answer 10

As with all hypothesis tests, the general purpose of the independent-measures t test is to determine whether the sample mean difference obtained in a research study indicates a real mean difference between the two populations (or treatments) or whether the obtained difference is simply the result of sampling error.

Question 11

Hypothesis Testing with the Independent- Measures t Statistic

Answer 11

The only difference between the t formula and the z-score formula is that the z-score uses the actual population variance, σ2 (or standard deviation), and the t formula uses the corresponding sample variance S (or standard deviation) when the population value is not known”

Question 12

Hypothesis Testing with the Independent- Measures t Statistic

Answer 12

For the independent t, G & W point out that it’s is technically a test of difference between sample mean difference and the hypothesized population mean difference …
Independent t Single sample (formula)

Question 13

Hypothesis Testing with the Independent- Measures t Statistic

Answer 13

Same logic behind hypothesis testing applied as with one sample
n However, important differences with two groups
q Incorporate2populationmeansintohypotheses
q Look at hypothetical distributions of sample mean differences when testing hypotheses

Question 14

Hypothesis Testing with the Independent- Measures t Statistic

Answer 14

Thus, estimated standard error of the mean includes 2 measures of variability and 2 sample sizes
q Degrees of freedom include the n of each group

Question 15

Hypothesis Testing with the Independent- Measures t Statistic

Answer 15

To prepare the data for analysis, the first step is to compute the sample mean and SS (or s, or s2) for each of the two samples.
n The hypothesis test follows the same four-step procedure outlined in Chapters 8 and 9.

Question 16

Hypothesis Testing with the Independent- Measures t Statistic

Answer 16

1. State the hypotheses and select an α level. For the independent-measures test, H0 states that there is no difference between the two population means.

Question 17

Hypothesis Testing with the Independent- Measures t Statistic

Answer 17

2. Locate the critical region. The critical values for the t statistic are obtained using degrees of freedom that are determined by adding together the df value for the first sample and the df value for the second sample. You then subtract two instead of one to reflect the two groups.

Question 18

Hypothesis Testing with the Independent- Measures t Statistic

Answer 18

3. Compute the test statistic. The t statistic for the independent- measures design has the same structure as the single sample t introduced in Chapter 9. However, in the independent-measures situation, all components of the t formula are doubled: 2 sample means, 2 population means, and 2 sources of error contributing to the standard error in the denominator.

Question 19

Table Slide 14

Answer 19

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Question 20

Hypothesis Testing with the Independent- Measures t Statistic

Answer 20

In order to calculate an independent samples t statistic, you’ll need to determine the difference between sample means and estimate the error term (estimated SEM)
q Two sources of error contributing to the standard error
in the denominator&raquo_space;
n To estimate the error term (s(M1-M2) in your text) you’ll need to know how to calculate pooled variance or pooled standard deviation

Question 21

Hypothesis Testing with the Independent- Measures t Statistic

Answer 21

q Pooled variance – a weighted average of the variance in each sample distribution
n Works for both = and ≠ size samples
n We assume samples come from populations with equal variances

Question 22

Hypothesis Testing with the Independent- Measures t Statistic

Answer 22

Given that our error term is typically defined as a standard deviation value divided by √n, it’s easy to see how to use the pooled variance or pooled standard deviation to estimate SEM (formula)

Question 23

Hypothesis Testing with the Independent- Measures t Statistic

Answer 23

Make a decision. If the t statistic ratio indicates that the obtained difference between sample means (numerator) is substantially greater than the difference expected by chance (denominator), we reject H0 and conclude that there is a real mean difference between the two populations or treatments.

Question 24

Hypothesis Testing with the Independent- Measures t Statistic

Answer 24

Note re: the t-table
q Whentargetdfavailableintable,noproblem
q When not available, need to estimate

Question 25

Hypothesis Testing with the Independent- Measures t Statistic

Answer 25

q Alwayserronthesideofconductingamoreratherthanless conservative test
q Iftargetdffallsbetweenavailabledfvalues,chooselowerdf (larger t critical value)

Question 26

Homogeneity of Variance Assumption

Answer 26

Althoughmosthypothesistestsarebuiltonasetofunderlying assumptions, the tests (including t tests) usually work reasonably well even if the assumptions are violated.
n Theoneimportantexceptionistheassumptionofhomogeneityof variance for the independent-measures t test.

Question 27

Homogeneity of Variance Assumption

Answer 27

n The assumption requires that the two populations from which the samples are obtained have equal variances.
n Thisassumptionisnecessarytojustifypoolingthetwosample variances and using the pooled variance in the calculation of the t statistic.

Question 28

Homogeneity of Variance Assumption

Answer 28

Before you can average (or pool) the two sample variances it is necessary that both samples are estimating the same population variance. See text for excellent discussion of this

Question 29

Homogeneity of Variance Assumption

Answer 29

Iftheassumptionisviolated,thenthetstatisticcontainstwo questionable values: (1) the value for the population mean difference which comes from the null hypothesis, and (2) the value for the pooled variance.

Question 30

Homogeneity of Variance Assumption

Answer 30

The problem is that you cannot determine which of these two values is responsible for a t statistic that falls in the critical region.
n In particular, you cannot be certain that rejecting the null hypothesis is correct when you obtain an extreme value for t.

Question 31

Homogeneity of Variance Assumption

Answer 31

If the two sample variances appear to be substantially different, you should use Hartley’s F-max test (sometimes called Levene’s test) to determine whether or not the homogeneity assumption is satisfied.
F-max = largest sample variance/smallest sample variance
s2 (largest)/s2 (smallest)

Question 32

Homogeneity of Variance Assumption

Answer 32

Compare with critical value (Table B.3)
n Violation of homogeneity assumption:
q F-max value > critical value
n If homogeneity of variance is violated, there is an alternative procedure that does not involve pooling the two sample variances.

Question 33

Measuring Effect Size for the Independent-Measures t

Answer 33

n Effectsizefortheindependent-measurestismeasured in mostly the same way that we measured effect size for the single-sample t
q estimate of Cohen’s d measures the size of the treatment effect in terms of the standard deviation
= Estimated mean difference / estimated standard deviation = M1 – M2 / √S2p

Question 34

Measuring Effect Size for the Independent-Measures t

Answer 34

q r2toobtainameasureofthepercentageofvarianceaccounted for by the treatment effect.
(formula)

Question 35

Measuring Effect Size for the Independent-Measures t

Answer 35

By measuring the amount of variability that can be attributed to the treatment, we obtain a measure of the size of the treatment effect. For the t statistic hypothesis test,

Question 36

Measuring Effect Size for the Independent-Measures t

Answer 36

t2 + df
percentage of variance accounted for =
r2 = ─────

Question 37

Summary of basic steps in hypothesis testing

Answer 37

n Identify IV DV & basic question being asked
n Establish hypotheses and alpha level
n Examine assumptions
q The data in each group is normally distributed
n descriptive statistics and graphs can help with this
q Homogeneity of variance (the variance in each is similar)

Question 38

Summary of basic steps in hypothesis testing

Answer 38

n Choose appropriate test to use
n Calculate test statistic and conduct significance test
n Calculateeffectsize(s)
n Write up and Interpret findings
q Conduct any other tests that seem relevant

Question 39

Describing Your Results Visually

Answer 39

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Question 40

Write up findings

Answer 40

An independent measures t test was conducted. As shown in Figure 1, a significant difference was found between eighth (M = 90.76, SD= 19.32) and tenth (M = 99.32, SD = 18.36) grade students in the interpretation of musical meaning, t(398) = 4.55, p < 0.05, d = 0.45. According to Cohen’s guidelines, this is a medium effect size

Question 41

Presenting results of the Independent t

test

Answer 41

independent measures t test found that the individuals under stress (M = 5.87, SD = 1.06) recalled significantly less digits than those not under stress (M = 6.80, SD = 1.32), t(28) = -2.13, d = 0.77. According to Cohen’s guidelines, this is a large effect, suggesting that stress can quite badly impair memory