Z-scores and Standardized Distributions

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```					                 Review for Exam #4
PSY 211
11-12-07

A. Highlights from this Section

Hypothesis Testing: 4 Steps

 Step 1: State hypotheses at the population level
o Null vs. Alternative hypothesis

 Step 2: Set critical region for sample
o z = ±1.96
o For t, based on df (n – 1), use table

 Step 3: Calculate sample statistics
o Use various z and t formulas
o OR use SPSS, read Output
o Calculate Cohen’s d, also

 Step 4: Report results in APA format
o If significant, report p < .05
o If non-significant, report ns
OR
o If using SPSS, you can report the exact
p value, if you like

o p is the probability that the results could
have occurred by sampling error, so low p
is good
o Large sample statistics (z or t) corresponds
to low p value
Old Pop Quiz

True Finding in
Population
No Effect       Some Effect

Accept Ho          (A)               (B)
Your
study
finding     Reject Ho,
(C)              (D)
Accept H1

Name A, B, C, and D.
You can use the following options:
“Correct Decision,” “Type I Error,” “Type II Error”

Distributions
Test                         Description              Ch.
Compare treated
z-test                       sample to untreated      7-8
population (σ known)
Compare treated
single sample t-test         sample to untreated      9
population (s known)
between-group t-test         Compare two different
10
(between-subject t-test)     groups of participants
Compare same group of
within-subject t-test
participants across two 11
(repeated-measures t-test)
time periods

ANOVA, chi square            Later in the semester
B. Sample Output

Analyses examining whether being born in Michigan
(Yes/No) relates to Anti-smoking attitude (7-pt scale)

Group Statis tics

Std. Error
14. Mic higan Born               N             Mean        Std. Deviation            Mean
71. Anti-s moking      No                                    72        5.583            2.0879                .2461
Yes                                  254        5.835            1.7660                .1108

Inde pe nde nt Sam ples Te st

Levene's Test
f or Equality of
V arianc es                                  t-test f or Equality of Means
95% Conf idence
Interval of the
Sig.         Mean        Std. Error         Dif f erence
F         Sig.            t        df      (2-tailed)   Dif f erence   Dif f erence   Low er        Upper
71.              Equal variances
6.548       .011      -1.022         324         .307        -.2513          .2458     -.7350        .2323
A nti-s moking   as sumed
Equal variances
-.931   101.547        .354        -.2513          .2699     -.7866        .2840
not assumed

What type of t-test is this?
Is the result statistically significant?
Is the result reliable?
What is the p-value?
What is the t-value?
What is the Cohen’s d?
What is the sample size?
Analyses comparing happiness before and after
Valentine’s Day among non-daters.

a
Paired Sam ples Statis tics

Std. Error
Mean                N           Std. Deviation      Mean
Pair    pre
baseline - happy            5.83                  333             1.547           .085
1       post 14 - happy
ac tual                     5.66                  333             1.748           .096
a. Date? - A verage of post- ratings = .00

a
Paired Sam ples Te st

Paired Dif ferences
95% Conf idence
Std.         Interval of the
Std.        Error           Dif f erence                           Sig.
Mean      Deviation     Mean        Low er        Upper        t      df    (2-tailed)
Pair
1
baseline - happy
pretualposthappy-
ac
- 14 -             .171           2.005        .110       -.045        .387    1.558   332        .120

a. Date? - Average of post- ratings = .00

What type of t-test is this?
Is the result statistically significant?
Is the result reliable?
What is the p-value?
What is the t-value?
What is the Cohen’s d?
What is the sample size?
C. Choosing the Correct Test

What statistical test would you likely use to determine
whether level of pain decreases from before treatment
to after treatment?

A. z-test
B. single-sample t-test
C. between group t-test
D. repeated measures t-test

To determine whether IQ scores differ between
cocaine users and the rest of the population, you
administer IQ tests to a sample of 10 cocaine users.
What statistical test would you likely use?

A. z-test
B. single-sample t-test
C. between group t-test
D. repeated measures t-test

You design a study to examine how gender
differences relate to changes in mood after eating
chocolate. Before eating chocolate, males and
females have similar mood. After eating chocolate
females are in a much better mood than males. How
could you analyze whether these post-chocolate
gender differences in mood are significant?

A. z-test
B. single-sample t-test
C. between group t-test
D. repeated measures t-test
D. Effect Size

r2 = 0.25
near-zero, small, medium, or large?

d = 0.25
near-zero, small, medium, or large?

r = -0.25
near-zero, small, medium, or large?

F. Calculations

Students randomly assigned to Study Group A
(n = 10) score an average of 80 points on a math
exam (SD = 10), and students in Study Group B (n =
10) score an average of 70 points on the same math
exam (SD = 12). Can we conclude that Study Group
A is reliably better than Study Group B? Write-up the
results in APA-format.

Before starting group treatment for alcohol abuse,
participants (n = 19) reported drinking an average of 8
drinks per day. Three participants failed to complete
the entire program. 6 months after treatment, those
completing the program reported drinking an average
of 3 drinks per day. In summary, on average, drinking
decreased by 5 drinks (SD = 2.0). Can we conclude
that the program decreases drinking? Write-up the
results in APA-format.

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