# Scales of Measurement - PowerPoint

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```							        Final Test Information
   The final test is Monday, April 13 at 8:30 am
   GRH102: Last name begins with A - I
   GRH106: Last name begins with K - Z
   The exam is out of 40: 15 multiple choice (worth
15); 5 short answer (worth 25)
   It will cover material from the entire course, but
the focus will be on ANOVA and correlation
   You will need to be able to identify when to do a
z-test, t-test, ANOVA, and correlation
   Not all of the short-answer questions require
calculations
   Statz Rappers
The Basics of Hypothesis Testing

1. State the null and research hypotheses in words and
symbols
2. Determine the level of significance
3. Identify the critical value
4. Calculate the test statistic
5. Evaluate the test statistic in light of the critical value
6. Make a decision about the null hypothesis
7. State your conclusions in plain language
Statistical Tests: Single sample mean

   Used to compare a single sample to a population
   Is the sample significantly different from the population?
H0: µ = X
H1: µ ≠ X
   If you know the population standard deviation, then
use a z-test
   If you do not know the population standard deviation,
then use a t-test
Statistical Tests: T-test for two related samples

   Used to compare two groups that are related in some
way
   Are the two groups significantly different from each other?
H0: µD = 0
H1: µD ≠ 0
   Could be a pre/post (i.e., before/after) design
   Could be two groups whose participants are related in
some way (couples, twins, siblings etc).
Statistical Tests: T-test for two independent
samples
   Used to compare two groups that are independent of
each other
   Are the two groups significantly different from each other?
Ho: µ1 = µ2
H1: µ1 ≠ µ2
Statistical Tests: Analysis of variance

   Used to compare three or more groups
   Are the groups significantly different from each other?
Ho: µ1 = µ2 = µ3
H1: µ1 ≠ µ2 ≠ µ3

   If you reject your null hypothesis and conclude that there
is a difference between the groups, you need to conduct
post hoc (Tukey HSD) tests to determine which groups
are different
ANOVA Summary Table
Source      df    SS          MS        F

Between     K-1   MSB*dfB     SSB/dfB   MSB/MSW

Within      N-K   MSW*dfW     SSW/dfW

Total       N-1   SSB + SSW
Statistical Tests: Correlation

   Used to determine if there is a relationships between two
variables
   Are the variables significantly correlated with each other?
H0: r = 0
H0: r ≠ 0
   There are three ways to describe the relationship between the
variables:
   The direction and strength of the relationship (i.e., is r positive or
negative, and how close is it to 1.0?)
   Is r significant (compare obtained value of r to critical value)?
   The amount of variance in one variable explained by the other (i.e., r2, the
coefficient of determination)
Study Designs
Experimental                       Correlational

   Looks for differences          Looks for relationships
between groups of scores        between groups of scores
   Uses terms like “effect”,
“difference”, “cause”          Uses terms like
“relationship”, “correlation”
   Use z-test, t-test or
ANOVA to analyze data          Use correlation to analyze
data
Data Analysis Decision Tree
for Experimental Designs

How many groups?

1 group (compare                      2 groups                           3 or moregroups
sample to population)                   Do a t-test                           Do an ANOVA

Do you know the population
standard deviation?
Are the scores related?                       Is Fobt ≥ Fcrit?

No                  Yes            No                 Yes                 No                  Yes
T-test for           Z-test for     T-test for                          Do not reject H0       Reject H0
T-test for related
single               single      independent                                                Conduct HSD
samples
samples              samples        samples                                                  post hoc test

```
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