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Independent Measures T-TestPowerPoint Presentation

Independent Measures T-Test

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Agenda

Agenda

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
- Compare to population with:
- Known µ
- Unknown

- This scenario is rare:
- Often researchers must collect data from two samples
- There are two possible scenarios

Introduction

- 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

Agenda

- Introduction
- The t Statistic for Independent-Measures
- Hypothesis Tests with Independent-Measures t-Test
- Instat
- Assumptions

Independent-Measures t-Test

- 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

Independent-Measures t-Test

- 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

Independent-Measures Designs

- Static-Group Comparison Design:
- Administer treatment to one group and perform posttest
- Perform posttest to control group
- Compare groups

X O

O

Independent-Measures Designs

- 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

Independent-Measures Designs

- 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

Agenda

- Introduction
- The t Statistic for Independent-Measures
- Hypothesis Tests with Independent-Measures t-Test
- Instat
- Assumptions

Hypothesis Test: Independent-Measures t-Test

- 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

Hypothesis Test: Independent-Measures t-Test

- 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

Hypothesis Test: Independent-Measures t-Test

- 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

Step 3: Collect Data and Calculate Statistic

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

Instat

- Type data from sample into a column.
- Label column appropriately.
- Choose “Manage”
- Choose “Column Properties”
- Choose “Name”

- Label column appropriately.
- Choose “Statistics”
- Choose “Simple Models”
- Choose “Normal, Two Samples”

- Choose “Simple Models”
- Layout Menu:
- Choose “Two Data Columns”

Instat

- Data Column Menu:
- Choose variable of interest

- Parameter Menu:
- Choose “Mean (t-interval)”

- Confidence Level:
- 90% = alpha 0.10
- 95% = alpha 0.05

Instat

- Check “Significance Test” box:
- Check “Two-Sided” if using non-directional hypothesis.
- Enter value from null hypothesis.

- If variances are unequal, check appropriate box
- Click OK.
- Interpret the p-value!!!

Reporting t-Test Results

- 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

Assumptions of Independent-Measures t-Test

- 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

Violation of Assumptions

- 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

Textbook Assignment

- Problems: 3, 11, 19

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