Summa Week 12 Flashcards
The _________________ t-test evaluates whether two independent groups or samples come from the same population
independent-samples t-test
A one-way between-subjects ANOVA is a generalization of a __________ t-test, and asks whether ___ or more (k) groups or samples come from the same ______
independent-samples t-test
three
population
What would a chart for a 1-way anova look like?
Subject Treatment 1 Treatment 2 Treatment 3
Subject 1 Subject 1 Subject 1 Subject 1
Subject 2 Subject 2 Subject 2 Subject 2
one-way anova summary table: between subjects
between group SSbetween?
dfbetween * MSbetween
one-way anova summary table: between subjects
dfbetween?
k - 1 (k = number of treatments)
one-way anova summary table: between subjects
MSbetween?
SSbetween/(k-1)
one-way anova summary table: between subjects
F-value?
MSbetween/MSwithin(or error)
one-way anova summary table: between subjects
SSerror?
dferror*MSerror
one-way anova summary table: between subjects
dferror?
N-k
one-way anova summary table: between subjects
MSerror?
SSerror/(N-k)
one-way anova summary table: between subjects
SStotal?
SSbetween subjects + SSerror
one-way anova summary table: between subjects
dftotal?
dfbetween + dferror
What is the design for using a One-way within-subjects ANOVA?
subjects undergo multiple conditions over time
What is the most powerful analysis for a 2-sample design?
matched-pair samples t-test
what is required for the matched-pair samples t-test to be the most powerful analysis for a 2-sample design?
if the samples are correlated. If they aren’t, then you can’t assume the difference is due to the conditions
True or false: repeated-measures designs (ANOVA) ask whether three or more (k) correlated groups or samples come from the same population.
True!
True or false: A One-way within-subjects ANOVA is a generalization of an independent samples t-test.
False! it is a generalization of a matched-pair samples t-test.
True or false: Repeated measures design can use family members instead of the same participants in research.
true. although the same participants is more helpful, similar individuals can be replaced, which refers to the whole “matched-pairs” idea
What does the one-way within-subjects ANOVA summary table look like, particularly for between subjects?
between/inter-subjects
SS between subjects / SSs / dfb (n-1) / MSb = NO F-VALUE OF INTEREST
What does the one-way within-subjects ANOVA summary table look like, particularly for treatment calculations?
treatment / differences due to treatment
SStreatment / SStreatment / dftreatment (k-1) / MStreatment / F=MStreatment/MSerror
What does the one-way within-subjects ANOVA summary table look like, particularly for error?
error = within/intra-subjects (individual) differences
Sourceerror / SSerror / (n-1)(k-1) / MSerror = NO F-VALUE CALCULATED
What is the difference between dfbetween for one-way between-subjects ANOVA and df between for one-way within-subjects ANOVA?
dfbetween-subjects = N-k dfwithin-subjects = (n-1)(k-1)
What does the one-way within-subjects ANOVA summary table look like, particularly for total SS?
Source total / SStotal / dftotal (n*k-1)
What is the difference between dftotal for one-way between-subjects ANOVA and dftotal for one-way within-subjects ANOVA?
dftotal between-subjects = N-1
dftotal within-subjects = n*k-1
Why are repeated-measures designs often more powerful?
because participants are measured more than one in order to better detect the individual differences and remove them from the analysis
How do you find individual differences in one-way within-subjects ANOVA?
subtracting them from the error term
What is the formula for repeated-measures design ANOVA (SS)?
SStotal = SSbetween subjects + SSwithin subjects (between treatments) + SSerror (individual differences)
What is the F-value for between-subjects in a one-way within-subjects ANOVA?
who cares? it isn’t relevant
What is the F-value for within-subjects in a one-way within-subjects ANOVA?
MSwithintreatment/MSerror(individual differences)
What the hell is Sphericity assumption?
tests for the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix (i.e. they are likely to occur from the same population)
What happens if a hypothesis of sphericity is not rejected (p > .05)?
we can conclude that sphericity assumption WAS met, and continue with repeated-measures ANOVA analysis
How do you determine covariance for subjects in a repeated-measures ANOVA design?
checking for assumption of Mauchly’s Test of Sphericity before reporting ANOVA results
What does Howell say sphericity assumption is?
the population variances of the repeated measurements are equal; the population correlations among all pairs of measures are equal
If a violation of the assumption of sphericity occurs, just write that it may have happened in results
False. It is a serious concern, which increases the potential for Type I error, so use a different estimate in determining new family-wise error for analysis
What are two estimates that can modify the severity of violation of sphericity assumption?
Greenhouse-Geisser, Huynh-Feldt and Lower-bound estimate
Which is more conservative: Greenhouse-Geisser or Huynh-Feldt for violation of sphericity assumption adjusted estimates?
Greenhouse-Geisser
What do you multiuply adjusted estimates of sphericity assumption by to correct for the effect of sphericity?
degrees of freedom
What do we assume about normality in one-way within-subjects ANOVA?
we assume they are normally distributed
What do we assume about independence in one-way within-subjects ANOVA?
it is NOT assumed that the scores are independent, since that’s what we’re basing our design off of
What does a one-way within-subjects ANOVA gave>?
Source SS df MS F
(Between) Subjects 486.11 8 - -
Treatment 2449.20 4 612.30 85.04
(Within)Error 230.40 32 7.20 -
Total 3166.31 44 - -
What are tests supplementing a within-subjects ANOVA similar to?
those for between-subjects ANOVA!
What is the difference in supplemental tets for within-subjects ANOVA and between-subjects ANOVA?
in the computational details in SPSS
True or false: When specific comparisons among means are made on between-subjects variables, an error term for each specific comparison is calculated. The same error term is used for all comparisons when the variable is within-subjects design.
False!
within-subjects variables need to compare each error term, whereas between-subjects designs are universally compared with the same error term
True or false: it is easy to explain if you have significant higher-order trends in within-subjects design.
Hell naw
Which factor do you use when reportin the results of within-subjects contrasts?
a) cubic
b) linear
c) quadratic
d) order 4
b) linear??????
What is another name for order effects?
trial effects
Does the order in which the participants receives a treatment affect how the participant behaves?
Yes!
What could be a cause for order effect?
the impact of practice effect, or the act of repeating the same task over and over and improving it due to regular practice
Other than practice, what can order effect do to repeated measures design tests?
the impact of fatigue effects, or decreased performance due to tiredness/less enthusiasm as the experiment continues, whether positive or negative
Other than practice and fatigue, what can order effect do to repeated measures design tests?
create (treatment) carry-over effects, with that of a treatment administered earlier persisting longer after to also influence proceeding treatments
Why do treatment carry-over effects create problems for within-subjects designs?
you may believe behaviour is due to treatment administered whereas it is due to a much earlier treatment influence still
Other than practice, fatigue, and carry-over effects, what can order effects be due to?
sensitization - participant may become sensitive to what the hypothesis is, and/or may behave differently after knowing what the hypothesis really is
Other than practice, fatigue, carry-over, and sensitization, what can order effect be due to?
sequence effects - if participant receives one sequence of treatments score differently than those participants who receive the treatment in a different sequence, there is an effect
e.g. the ability to assess the sequence effects can answer the question: “Does getting the treatments in one particular sequence cause a group to score higher than a groupgetting the treatments in a different sequence”?
True or false?An ANOVA determines which group means significantly vary in the population, and also determines the size of the deviation in the population by comuting a measure of effect size called proportion of deviation
False. Although similar, it determines size of variance and proportion of variance
What does proportion of variance measure in ANOVA?
how much variability in the DV can be accounted for by the levels of the factor
What are two measures of proportion of variance used in within-subjects design?
partial eta-squared, and partial omega-squared
What is the power of one-way within-subjects ANOVA based on?
the assumption that observing the same participants across groups will results in more consistent responding or changes in the DV, between groups
T or F: the within-subjects design is associated with more power to detect an effect than the between-subjects design
true
Why is the within-subjects design is associated with more power to detect an effect than the between-subjects design?
some of the error in the denominator of the test stat is remover, however it is only true when responding between-groups is CONSISTENT
T or F: the within persons variation is measured and subtracted from the error term in the denominator for one-way within-subjects ANOVA.
false. the between-persons variation is eliminated, which increases the power of the test by looking only at individual differences
True or False: For ANOVA, you can adjust the df so subtracting the between persons variation will not always increase the power of a one-way within-subjects ANOVA.
true
How to support results of a one-way within subjects ANOVA (step 1):
report the test stat, df, and p value
How to support results of a one-way within subjects ANOVA (step 2):
report the effect size for significant analyses (partial eta squared or partial omega squared)
How to support results of a one-way within subjects ANOVA (step 3):
the means, SD measured in a study can be summarized in a figure or table or in the main text of the article
How to summarize the results of a posthoc within-subjects design test:
identify which posthoc test you computed and the p value for significant results
Example of reporting within-subjects one-way analysis of variance…
A within-subjects one-way analysis of variance showed that ratings of effectiveness for one or three advertisements significantly varied, F(2, 12) = 17.38, p < .05, np^2 = 0.69. Using the Bonferroni procedure, related sample t-tests showed that ratings of effectiveness were significantly greater for the ad with smoking-related cues compared to the ad with generic cues and the ad with no cues (p < .05). Otherwise, no significant differences were evident (p > .05). The means and standard deviations for each group are shown in table…
CHI‐SQUARE TESTS
A general purpose test for use with discrete/nominal
variables
Chi-square tests: Focus on the number of different categories
Categories have no order relation (larger/smaller) to each
other (e.g., male/female; university major)
Chi-square tests: Focus on the number of different categories
Numbers representing categories (e.g., 1= psychology major,
2 = sociology major, 3 = other) cannot be added, subtracted,
multiplied or divided. BUT the counts of the number of
people in each category can be added, subtracted, multiplied
and divided
Chi-square tests: assumptions of random sampling
Each sample is a random sample from its population Considered inappropriate to conduct if violated, but some argue it is robust if violated
Chi-square tests: assumption of independence of cases
each case is not influenced by other cases, not robust
Chi-square tests: expected frequencies assumption
All cells must have expected frequencies of at least 5, or at least 5 times as many individuals as categories (or cells) Not robust to violations
Chi-square test formula (x^2)
x^2 = sum of (O-E)^2/E
observed - error
Chi square distribution looks like
positively-skewed data that goes downward for 1, but then has hills from 0 up and then down as a positive skew
Two kinds of chi square tests
Distribution shape tests
Goodness of fit test or one way classification test
Homogeneity test
Independence tests
Or contingency table tests (a*b tables)
These are often incorrectly called ʺassociation testsʺ (they
are really another kind of goodness of fit test) or ʺTwoway
classificationʺ tests
Both two kinds of tests compare the observed frequency of
categories with an expected frequency of categories
The expected frequencies are usually derived from the null
hypothesis. But they need not be derived from the null. They
can be derived from almost any theory you want to consider
Chi square test levels of a single nominal variable
x^2 = sum of (O-E)^2/E
Chi-square test in SPSS
- Data - Weight cases to determine influence
2. Analyze - nonparametric tests - legacy dialogs - chi-square
What do you report from SPSS for Chi-square tests?
test statistics chi-square x.xxx^a, df 1, asympt. sig. (significance level!) = .xxx
Do you indicate the observed or the expected in APA?
the expected, since you get the observed in your test
Chi-square test calculation value (the goal of finding out the expected frequencies of = IV1 is associated with __times higher/lower than IV2)
x^2 = (observed1 - expected1)^2/expected1 + (observed2 - expected2)^2/expected2
Can Chi-square tests be negative?
hell naw
How do we determine independence in chi-square tests?
a contingency table between the two NOMINAL variables in the various categories
Determining expected frequencies formula
E = (Row/N)Column
= (Rowmarginal mean/Ntotal)Column marginal mean
e.g. expected frequency of night people taking their own car
= (Night Row marginal mean 80/200 people total)own car marginal mean 70
= 28
What is the df for Chi-square tests?
df = (Ncolumn - 1) (Nrows - 1)
What do you report for Chi square tests?
x^2(df) = x.xx
What is an alternative to Pearson’s chi-square?
likelihood ratio test
What is the likelihood ratio test based on?
a maximum-likelihood theory
What is the first step for the likelihood ratio test?
create a model for which the probability of obtaining the observed set of data is maximized
What is the second step for the likelihood ratio test?
this model is compared to the probability of obtaining those data under the null hypothesis
What is the third step for the likelihood ratio test?
the resulting statistic compareds observed frequencies with those predicted by the model
i and j are the rows and columns of the contingency table, and ln is the natural logarithm
G = 2 (sum of observeij * (Observeij/Expectedij)
What has a sampling distribution that approximates the Chi-square distribution?
the G statistic
How does the G stat sampling distribution approximate the Chi-square distribution?
it approximates it with (r-1)(c-1) degrees of freedom when expected values in all cells >=5
What are expected values in all cells when approximating the Chi-square distribution?
5
What test is preferred with small sample sizes: Pearson’s chi-square or likelihood ratio test?
likelihood ratio test
Using the following data, how would you compare Chi square and G?
O <25 y.o >25 y.o. Total
Male 31(27.7) 5(8.3) 36
Female 42(45.3) 17(13.7) 59
Total 73 22 95
X^2 = (31-27.7)^2/27.7 + (5-8.3)^2/8.3 + (42-45.3)^2/45.3 + (17-13.7)^2/13.7
= 0.40 + 1.34 + 0.25 + 0.81
= 2.80
G = 2 x (31ln(31/27.7) + 5ln(5/8.3) + 42 * ln(42/45.3) + 17ln(17/13.7))
= 2 * (3.49 - 2.53 - 3.18 + 3.67)
= 2.90
df = (r-1) (c-1) = (2-1)(2-1) = 11 = 1
After entering data in SPSS for a likelihood-ratio test, what do you do next?
weight cases by selecting Data, then weight cases as the frequencies
What do you do in SPSS for a likelihood-ratio test once you’ve weighed the cases?
Select Analyze, then descriptive statistics, and in the Crosstabs area put the variables into the boxes and click Statistics, and select “Chi-square and Phi and Cramer’s V”
Why do we want to test Chi-square for Cramer’s V?
to determine the effect size when NOT using a 2x2 table
What is a d-family effect size for Chi-square tests?
based on one or more measures of the differences between groups or levels of the independent variable
What is an effect size for Chi-square tests that is some sort of correlation coefficient between two IVs?
an r-family effect size
Who typically uses odds ratio tests?
medical professionals
How do you determine the d-family effect size (risk ratio or relative risk) ?
RR = risk of no treatment / Risk with treatment
= proportion/proportion
= ____ times higher/lower if you DON’T use the treatment than if you
What is an odds ratio?
An odds ratio, or effect size d-family refers to the odds of something occurring with treatment divided by the number with the result not occurring
e.g. the odds of having a heart attack for a member of the aspirin group is the number having a heart attack divided by the number not having a heart attack
What is the odds ratio/d-family effect size formula?
OR = odds| no treatment/odds| with treatment
= the odds of a heart attack given that you did not take aspirin were 189/10,845 =0.0174. The odds of a heart attack given that you DID take aspirin were 104/10,933 = 0.0095. the odds ratio is simply the ratio of these two odds. The odds of a heart attack without aspirin are 1.83 times higher than the odds of a heart attack with aspirin.
Why does Howell favour the odds ratio method?
a) the odds ratio method can calculate situations in which a true risk ratio cannot occur/low probability events, and
b) taking the natural log of the odds ratio [ln(OR)] gives a stat that is useful in a variety of situations such as logistic regression and log-linear models
What is Phi effect size?
an effect size used in Chi-square tests (nominal x nominal) that represents the correlation between two variables and applies only to 2x2 tables
In reporting the chi-square test, what do you report to summarize the goodness-of-fit?
test statistic, df, and p value
In reporting the chi-square test, how can observed frequencies be summarized?
in a figure or table or in the main text
In reporting the chi-square test, what else would you use to summarize the test for independence?
the effect size i.e. Cramer’s V or phi square test
Written summary of a chi-square test for independence
The chi-square test for independence showed a significant relationship between the type of counseling and outcome, x^2 (1, N = 300) = 5.39, p = .020, Cramer’s V = 0.22. The data indicates that family involvement in counseling is associated with a greater number of patients completing counseling.
____ and _____ frequencies are used in the calculation of the x^2 statistic.
observed and expected?
When frequency data are collected, we use the _____ to determine how well an observed frequency distribution of two nominal variables fits some expected breakdown.
???
True or false?: the value of df for a chi-square test does not depend on the sample size (n).
False?
True or false?: A positive value for the chi-square statistic indicates a positive correlation between the two variables.
True?
Which of the following is an assumption of x^2 tests?
a. it is a parametric test
b. it is appropriate only for ordinal data
c. the frequency in each cell should be less than 5
d. the sample should be randomly selected
c. the frequency in each cell should be less than 5
The calculation of the df for the _____ is (r-1) (c-1)
a. independent-groups t-test
b. correlated-groups t-test
c. x^2 test of independence
d. Wilcoxon rank-sum test
c. x^2 of independence?
