Independent Measures T-Test Quantitative Methods in HPELS 440:210.
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Transcript of Independent Measures T-Test Quantitative Methods in HPELS 440:210.
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 sampleCompare to population with:
Known µ Unknown
This scenario is rare:Often researchers must collect data from two
samplesThere 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) = √s2
p/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
Recall General Process:1. State hypotheses
State relative to the two samples No effect samples will be equal
2. Set criteria for decision making3. Sample data and calculate statistic4. Make decision
Hypothesis Test: Independent-Measures t-Test
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?
1.734
Step 1: State Hypotheses
Non-Directional
H0: µ1 = µ2
H1: µ1 ≠ µ2
Directional
H0: µ1 ≤ µ2
H1: µ1 > µ2
Step 2: Set Criteria
Alpha () = 0.05
Degrees of Freedom:
df = (n1 – 1) + (n2 – 1)
df = (10 – 1) + (10 – 1) = 18
Critical Values:
Non-Directional 2.101
Directional 1.734
Step 4: Make Decision
Accept or Reject?
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 + s2
p / 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
Agenda
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”
Choose “Statistics”Choose “Simple Models”
Choose “Normal, Two Samples”
Layout Menu: Choose “Two Data Columns”
Instat
Data Column Menu:Choose variable of interest
Parameter Menu:Choose “Mean (t-interval)”
Confidence Level:90% = alpha 0.1095% = 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 More on this later
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).
Agenda
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 designScale of measurement assumption violation:
Ordinal data
Normality assumption violation: Regardless of scale of measurement
Textbook Assignment
Problems: 3, 11, 19