independent measures t test
Download
Skip this Video
Download Presentation
Independent Measures T-Test

Loading in 2 Seconds...

play fullscreen
1 / 26

Independent Measures T-Test - PowerPoint PPT Presentation


  • 79 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Independent Measures T-Test' - randall-hampton


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
independent measures t test

Independent Measures T-Test

Quantitative Methods in HPELS

440:210

agenda
Agenda
  • Introduction
  • The t Statistic for Independent-Measures
  • Hypothesis Tests with Independent-Measures t-Test
  • Instat
  • Assumptions
introduction
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
introduction1
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
agenda1
Agenda
  • Introduction
  • The t Statistic for Independent-Measures
  • Hypothesis Tests with Independent-Measures t-Test
  • Instat
  • Assumptions
independent measures t test1
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 test2
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
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 designs1
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 designs2
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

agenda2
Agenda
  • Introduction
  • The t Statistic for Independent-Measures
  • Hypothesis Tests with Independent-Measures t-Test
  • Instat
  • Assumptions
hypothesis test independent measures t test
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 test1
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 test2
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?
slide16

Step 1: State Hypotheses

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

slide17

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?

agenda3
Agenda
  • Introduction
  • The t Statistic for Independent-Measures
  • Hypothesis Tests with Independent-Measures t-Test
  • Instat
  • Assumptions
instat
Instat
  • 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”
  • Layout Menu:
      • Choose “Two Data Columns”
instat1
Instat
  • Data Column Menu:
    • Choose variable of interest
  • Parameter Menu:
    • Choose “Mean (t-interval)”
  • Confidence Level:
    • 90% = alpha 0.10
    • 95% = alpha 0.05
instat2
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
    • More on this later
  • Click OK.
  • Interpret the p-value!!!
reporting t test results
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).
agenda4
Agenda
  • Introduction
  • The t Statistic for Independent-Measures
  • Hypothesis Tests with Independent-Measures t-Test
  • Instat
  • Assumptions
assumptions of independent measures t test
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
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
Textbook Assignment
  • Problems: 3, 11, 19
ad