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# Independent Measures T-Test - PowerPoint PPT Presentation

Independent Measures T-Test. Quantitative Methods in HPELS 440:210. Agenda. Introduction The t Statistic for Independent-Measures Hypothesis Tests with Independent-Measures t-Test Instat Assumptions. Introduction. Recall  Single-Sample t-Test: Collect data from one sample

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### Independent Measures T-Test

Quantitative Methods in HPELS

440:210

• Introduction

• The t Statistic for Independent-Measures

• Hypothesis Tests with Independent-Measures t-Test

• Instat

• Assumptions

• Recall  Single-Sample t-Test:

• Collect data from one sample

• Compare to population with:

• Known µ

• Unknown 

• This scenario is rare:

• Often researchers must collect data from two samples

• There are two possible scenarios

• Scenario #1:

• Data from 1st sample are INDEPENDENT from data from 2nd

• AKA:

• Independent-measures design

• Between-subjects design

• Scenario #2:

• Data from 1st sample are RELATED or DEPENDENT on data from 2nd

• AKA:

• Correlated-samples design

• Within-subjects design

• Introduction

• The t Statistic for Independent-Measures

• Hypothesis Tests with Independent-Measures t-Test

• Instat

• Assumptions

• Statistical Notation:

• µ1 + µ2: Population means for group 1 and group 2

• M1 + M2: Sample means for group 1 and group 2

• n1 + n2: Sample size for group 1 and group 2

• SS1 + SS2: Sum of squares for group 1 and group 2

• df1 + df2: Degrees of freedom for group 1 and group 2

• Note: Total df = (n1 – 1) + (n2 – 1)

• s(M1-M2): Estimated SEM

• Formula Considerations:

• t = (M1-M2) – (µ1-µ2) / s(M1-M2)

• Recall  Estimated SEM (s(M1-M2)):

• Sample estimate of a population  always error

• SEM measures ability to estimate the population

• Independent-Measures t-test uses two samples therefore:

• Two sources of error

• SEM estimation must consider both

• Pooled variance (s2p)

• SEM (s(M1-M2)):

• s(M1-M2) = √s2p/n1 + s2p/n2 where:

• s2p = SS1+SS2 / df1+df2

• Static-Group Comparison Design:

• Administer treatment to one group and perform posttest

• Perform posttest to control group

• Compare groups

X O

O

• Quasi-Experimental Pretest Posttest Control Group Design:

• Perform pretest on both groups

• Administer treatment to treatment group

• Perform posttests on both groups

• Compare delta (Δ) scores

O X O  Δ

O O  Δ

• Randomized Pretest Posttest Control Group Design:

• Randomly select subjects from two populations

• Perform pretest on both groups

• Administer treatment to treatment group

• Perform posttests on both groups

• Compare delta (Δ) scores

R O X O  Δ

R O O  Δ

• Introduction

• The t Statistic for Independent-Measures

• Hypothesis Tests with Independent-Measures t-Test

• Instat

• Assumptions

• Recall  General Process:

• State hypotheses

• State relative to the two samples

• No effect  samples will be equal

• Set criteria for decision making

• Sample data and calculate statistic

• Make decision

• Example 10.1 (p 317)

• Overview:

• Researchers are interested in determining the effect of mental images on memory

• The researcher prepares 40 pairs of nouns (dog/bicycle, lamp/piano . . .)

• Two separate groups (n1=10, n2=10) of people are obtained

• n1 Provided 5-minutes to memorize the list with instructions to use mental images

• n2 Provided 5-minutes to memorize the list

• Researchers provide the first noun and ask subjects to recall second noun

• Number of correct answers recorded

• Questions:

• What is the experimental design?

• What is the independent variable?

• What is the dependent variable?

Non-Directional

H0: µ1 = µ2

H1: µ1≠ µ2

Directional

H0: µ1≤ µ2

H1: µ1 > µ2

Degrees of Freedom:

df = (n1 – 1) + (n2 – 1)

df = (10 – 1) + (10 – 1) = 18

Critical Values:

Non-Directional  2.101

Directional  1.734

Step 2: Set Criteria

Alpha (a) = 0.05

1.734

Pooled Variance (s2p)

s2p = SS1 + SS2 / df1 + df2

s2p = 200 + 160 / 9 + 9

s2p = 360 / 18

s2p = 20

SEM (s(M1-M2))

s(M1-M2) = √s2p / n1 + s2p / n2

s(M1-M2) = √20 / 10 + 20 / 10

s(M1-M2) = √2 +2

s(M1-M2) = 2

t-test:

t = (M1-M2) – (µ1-µ2) / s(M1-M2)

t = (25-19) – (0-0) / 2

t = 6 / 2 = 3

Step 4: Make Decision

Accept or Reject?

• Introduction

• The t Statistic for Independent-Measures

• Hypothesis Tests with Independent-Measures t-Test

• Instat

• Assumptions

• Type data from sample into a column.

• Label column appropriately.

• Choose “Manage”

• Choose “Column Properties”

• Choose “Name”

• Choose “Statistics”

• Choose “Simple Models”

• Choose “Normal, Two Samples”

• Choose “Two Data Columns”

• Choose variable of interest

• Choose “Mean (t-interval)”

• Confidence Level:

• 90% = alpha 0.10

• 95% = alpha 0.05

• Check “Significance Test” box:

• Check “Two-Sided” if using non-directional hypothesis.

• Enter value from null hypothesis.

• If variances are unequal, check appropriate box

• More on this later

• Click OK.

• Interpret the p-value!!!

• How to report the results of a t-test:

• Information to include:

• Value of the t statistic

• Degrees of freedom (n – 1)

• p-value

• Examples:

• Girls scored significantly higher than boys (t(25) = 2.34, p = 0.001).

• There was no significant difference between boys and girls (t(25) = 0.45, p = 0.34).

• Introduction

• The t Statistic for Independent-Measures

• Hypothesis Tests with Independent-Measures t-Test

• Instat

• Assumptions

• Independent Observations

• Normal Distribution

• Scale of Measurement

• Interval or ratio

• Equal variances (homogeneity):

• Violated if one variance twice as large as the other

• Can still use parametric  with penalty

• Nonparametric Version  Mann-Whitney U (Chapter 17)

• When to use the Mann-Whitney U Test:

• Independent-Measures design

• Scale of measurement assumption violation:

• Ordinal data

• Normality assumption violation:

• Regardless of scale of measurement

• Problems: 3, 11, 19