Z-scores and Standardized Distributions

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Z-scores and Standardized Distributions Powered By Docstoc
					                 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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