Download PL2131 Statistical Tests Summary

PL2131 Statistical Tests Summary
Hypothesis Testing: The Process
1. Restate the question as a research hypothesis and a null hypothesis about the populations.
Population 1:
Population 2:
Research hypothesis (Ha):
Null hypothesis (Ho):
2. Determine the characteristics of the comparison distribution.
Determine mean (μ) and standard deviation (σ) OR df.
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should
be rejected.
Refer to statistical tables to determine the cutoff sample score.
4. Determine your sample’s score on the comparison distribution.
Calculate the relevant statistic.
5. Decide whether to reject the null hypothesis.
Compare the statistics from steps (4) and (5). Check if it is extreme (statistically significant) enough
at the 5% significance level to reject the null hypothesis and support the research hypothesis.
Hypothesis Testing: Specific Tests
Test
Characteristics & Steps
Z-test
 Comparing an individual score or sample mean against
comparison distribution.
 Known comparison mean and variance.
 (4) Calculate sample Z score.
 If comparing sample mean, comparison distribution
must be a distribution of means.
 Comparison mean = population mean.
 (2) μM = μ =
 (2) Calculate comparison standard deviation (σM).
One-sample
T-test
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Dependentsamples
T-test
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Independentsamples
T-test
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Comparing sample mean against comparison
distribution.
Known comparison mean but unknown variance.
Comparison mean = population mean.
(2) μM = μ =
(2) Calculate comparison standard deviation (SM).
(3) Top 5% of scores begin at a t score of about ____.
(4) Calculate sample t score.
Comparing two related sample means. (Withinsubjects design.)
Known comparison mean but unknown variance.
Assume comparison mean = 0. (No difference.)
(2) μM = μ = 0
(2) Calculate comparison standard deviation (SM).
(3) Top 5% of scores begin at a t score of about ____.
(4) Calculate sample t score.
Comparing two independent sample means. (Betweensubjects design.)
Known comparison mean but unknown variance.
Assume comparison mean = 0. (No difference.)
(2) μM = μ = 0
(2) Calculate comparison standard deviation (SDifference).
(3) Use dfTotal when checking the t table.
(3) Top 5% of scores begin at a t score of about ____.
(4) Calculate sample t score.
Formulae
Correlation
and Simple
Regression
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Testing the significance of a correlation coefficient (r).
(1) Population 1: People like those in this study.
(1) Population 2: The general population for whom…
(2) Calculate df.
(3) Top 5% of scores begin at a t score of about ____.
(4) Calculate correlation coefficient (r).
(4) Calculate sample t score.
Chi-square
Test for
Goodness of
Fit
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Compare how well an observed breakdown of people
over various categories fits some expected breakdown.
Single nominal variable.
(2) Calculate df.
(3) The point of extremity begins from a Chi-Square
score of about ___ onwards.
(4) Calculate sample Chi-Square score.
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Chi-square
Test for
Independence
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Compare how well an observed breakdown of people
over various categories fits some expected breakdown.
Two nominal variables.
(2) Calculate df.
(3) The point of extremity begins from a Chi-Square
score of about ___ onwards.
(4) Calculate sample Chi-Square score.
Dependent-samples T-test Tabulation
Participant
Score
Difference
Deviation
Squared Deviation
Before After (After – Before) (Difference – M)
1
2
3
Σ:
Independent-samples T-test Tabulation
Experimental Group
Score Deviation (X – M)
Squared Deviation
Score
Control Group
Deviation (X – M)
Squared Deviation
Σ:
Correlation Tabulation
X
Y
X – MX
(X – MX)2
Y – MY
(Y – MY)2
(X – MX)(Y – MY)
Σ:
Chi-square Test for Goodness of Fit Tabulation
Category O
E
O–E
(O – E)2
(O – E)2/E
A
B
C
Σ:
Chi-square Test for Independence Tabulation
∑(𝑶 − 𝑬)𝟐
A
B
Total
𝑿𝟐 =
1
OA1 (EA1) OB1 (EB1)
R1
𝑬
(𝑶𝑨𝟏 − 𝑬𝑨𝟏 )𝟐 (𝑶𝑩𝟏 − 𝑬𝑩𝟏 )𝟐 (𝑶𝑨𝟐 − 𝑬𝑨𝟐 )𝟐 (𝑶𝑩𝟐 − 𝑬𝑩𝟐 )𝟐
2
OA2 (EA2) OB2 (EB2)
R2
=
+
+
+
𝑬𝑨𝟏
𝑬𝑩𝟏
𝑬𝑨𝟐
𝑬𝑩𝟐
Total
CA
CB
N