# Statistics &amp; research

## Terms

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1) variable that can be controlled
2) variable that cannot be controlled
3) what is the limitation associated with the latter
1) manipulated variables
2) organismic variables
3) cannot determine if relationships between variables are CAUSAL in nature
1) observing a behavior for a period of time, divided into equal periods (30-min periods divided into 15-sec)
2) observing a behavior each time it occurs
3) observing a behavior in a number of settings
4) coding behavioral sequences rather
1) interval recording
2) event sampling (recording)
3) situation sampling
4) sequential analysis
how does quasi differ from true experimental research?
in quasi, researcher CANNOT control the ASSIGNMENT of subjects to treatment groups
random assignment vs. random selection
1) which allows researcher to GENERALIZE findings from sample to population
2) which allows researcher to be more certain that effect on DV was CAUSED by IV
1) random selection
2) random assignment
Sampling (selection) techniques:
1) selecting units of individuals rather than individuals
2) every member of population has equal chance of being in sample
3) dividing population into groups (acc to similar characteristics) and randomly s
1) cluster sampling
2) simple random sampling
3) stratified random sampling
4) cluster sampling
to obtain a sample of elementary school kids, you randomly select several schools and then randomly choose students from schools selected. What type of sampling?
cluster sampling
which type of behavioral sampling is most useful for studying behaviors that leave a permanent record?
event recording
good for behaviors that occur infrequently, have a long duration, or leave permanent record (e.g., test)
3 factors that can cause variability in DV
1) IV (experimental variance)
2) systematic error (due to extraneous variables)
3) random error (due to random fluctuations)
1) What type of variance does a researcher want to maximize?
2) To minimize?
3) To control?
1) experimental variance (due to IV)
2) random error
3) systematic error
Techniques for controlling effects of extraneous variable:
1) what type of assignment?
2) holding extraneous variable ___
3) making groups equivalent in terms of status on variable, then randomly assigning (what is this called)
4) inc
1) random assignment of subjects to tx groups (randomization)
2) constant (but limits generalizability)
3) matching subjects
4) blocking - not individually matched, but blocked (grouped) on basis of status on extraneous variable (e.g., group subjects by level of sx severity -mild, mod, severe- THEN randomly assign)
5) ANCOVA
internal validity allows the researcher to determine ___
if there is a CAUSAL relationship between IV and DV
types of extraneous variables:
1) biological or psychological change that occurs within subject during course of study as a fx of time
2) when an external event systematically affects status of subjects on DV
3) changes in accuracy/sensiti
1) maturation
2) history
3) instrumentation
4) statistical regression
5) testing
6) attrition (mortality)
7) selection
Difference between history and maturation
history comes from "out there" and occurs at same time that IV is adminstered

maturation reflects change within subjects as a result of passage of time
2) what type of design can control for these effects
2) single-group time-series design - measures DV several times at regular intervals before and after intervention is applied
studies that examine relationship btwn IV and DV in a lab or non-naturalistic setting
analogue studies
external validity is limited by ___
internal validity
1) what is pretest sensitization?
2) what does it threaten?
3) what type of research design can control for it? How?
1) administration of pretest can sensitize subjects to purpose of research and alter reaction to IV
2) external validity (generalizability)
3) Solomon four-group design - treats pretest as an additional IV
when subjects are volunteers, this affects generalizability due to the interaction btwn ___ and ___
selection and treatment
1) when a participant responds in a particular way simply b/c they are being observed
2) cues in experimental setting that inform subjects of purpose of study or suggest what behaviors are expected
3) experimenter unintentionally provides subje
1) reactivity
2) demand characteristics
3) experimenter expectancy
4) single-blind or double-blind study
1) when study exposes subject to 2+ levels of IV, effects of one level of IV can be affected by previous exposure to another level. What is this called (3 names)
2) what type of design can control for this? how?
1) multiple treatment interference, order effect, carryover effects
2) counterbalanced design
different subjects receive levels of the IV in different orders (ex of counterbalanced design = Latin square design)
When using the ANCOVA, the covariate is ___
the extraneous variable
extraneous variables correlate with the IV or DV
DV
Counterbalancing is used to control ___
order effects (aka carryover effect, multiple tx interference)
1) whenever a study includes 2 or more IVs, it is called a ___
2) it allows researcher to analyze __ and __
1) factorial design
2) main effects of each IV; interaction btwn IV's
1) what is a main effect?
2) when does an interaction occur?
3) if a conclusion is made on the basis of main effects, what effect will an interaction likely have?
1) effect of ONE IV on the DV (disregarding the effects of all other IV's)
2) when the effects of an IV DIFFER at different level of ANOTHER IV
3) modify or invalidate those conclusions
1) what type of design involves measuring DV several times at regular intervals BOTH before and after the tx is applied
2) what is the control group?
3) what is the biggest threat to internal validity?
4) what is the biggest threat to exte
1) single-group time-series design
2) subjects act as their OWN no-tx controls
3) history
4) carryover effects
5) maturation (since they occur gradually over time)
6) autocorrelation
autocorrelation
1) what is it
2) what effect does it have on the value of the inferential statistic
3) what type of error is associated
1) when subject's performance on post-tests is likely to correlate with performance on pre-tests
2) inflates it
3) increases probability of Type I error
1) a mixed design combines __ and __
2) common in research studies that involve ___
3) what becomes the additional IV
1) between-groups and within-subjects
2) measuring DV over time or across trials
3) time or trials can become an additional IV and is considered a within-subjects variable
what is another name for repeated measures design
within-subjects design
single-subject designs
1) includes __ and __
2) in an AB design, the DV is measured how often?
3) what are other names for ABA or ABAB designs? (2)
4) what is a major advantage of these (ABA, ABAB) designs?
5) when are these desi
1) at least one baseline phase and one tx phase
2) regular intervals
3) reversal designs or withdrawal designs
4) can be more certain that observed change in DV is actually due to IV (rather than extraneous factor)
5) when withdrawal of a tx during course of study is unethical
1) when might a multiple baseline design be used
2) how is the tx applied
1) when a reversal design is inappropriate
2) sequentially applying in one of 3 ways:
a) to different behaviors of same subject (mult base across beh)
b) same subject in different settings (mult base across settings)
c) same behavior of different subjects (mult base across subjects)
2) when using a multiple baseline design, a tx is __ applied to different baselines
1) IV's
2) sequentially
what are these used for:
1) descriptive statistics
2) inferential statistics
1) describe and summarize data
2) determine if sample values can be generalized to population
type of variable
1) can take on an infinite number of values
2) can assume only a finite number of values
1) continuous variable
2) discrete variable
Nominal scale
1) divides variable into __
2) what mathematical operation can be performed
1) unordered categories
2) only to count FREQUENCY

(e.g., gender, religion, DSM dx)
Ordinal scale
1) divides observations into __
2) limitation
1) categories that can be ordered
2) do not tell HOW MUCH difference is btwn scores (can't conclude that rank of 10 is twice the rank of 5)

(e.g., rank, Likert, college level - fresh, soph)
Interval scale
1) has the properties of __ and __
2) what mathematical operations can be performed
1) order and equal intervals

(e.g., IQ, temperature, standardized test scores)
Ratio scale
1) has what 3 properties
2) what mathematical operations can be performed
1) order, equal intervals, absolute zero point
2) also multiplication and division (can say that one value is twice another)

(e.g., Kelvin temperature, # calories consumed, # correct test items, reaction time in seconds)
On a graph (frequency polygon), what is plotted on the:
1) horizontal (abscissa) axis
2) vertical (ordinate) axis
1) scores
2) frequencies
1) In describing distributions, what term refers to the peakedness (height or flatness) of a distribution

What type of distribution is:
1) more "peaked"
2) flatter
3) normal
1) kurtosis
2) leptokurtic
3) platykurtic
4) mesokurtic
What type of skew:
1) most scores fall in the negative side of the distribution
2) most fall in the positive side
1) positively skewed
2) negatively skewed
describe the following measures of central tendency:
1) mode
2) median
3) mean
1) most frequently occuring score
2) divides distribution in half
3) average of scores
1) in a skewed distribution, which is the best measure of central tendency
2) which is least susceptible to sampling fluctuations
3) when a distribution is skewed, how will this affect the mean
1) median (insensitive to outliers)
2) mean
3) the mean will be pulled toward the tail of the distribution
measures of variability
1) calculated by subtracting lowest score from highest
2) the average amount of variability in a distribution
3) a measure of variability (dispersion) around the mean
1) range
2) variance
3) SD
mathematically, how are the variance and SD related
SD = square root of variance
or
variance = SD squared
Constants
when adding/subtracting a constant to every score in a distribution, what effect on:
1) measures of central tendency
2) measures of variability

when multiplying/dividing each score in a distribution by a constant, what
1) increase/decrease
2) no change

3) increase/decrease
4) increase/decrease
central limit theorem applies to what type of distribution
sampling distribution
(frequency distribution of the means of a large number of equal size samples from a population)
central limit theorem
what are the three predictions
1) regardless of shape of distribution of scores in population, as sample SIZE increases, the sampling distribution of mean approaches a normal distribution
2) mean of sampling dist of mean = population mean
3) SD of sampling dis of mean = population SD divided by square root of sample size
1) what is the standard error of the mean
2) the variability is due to the effects of __
3) what is the formula
1) estimate of extent to which the mean of any one sample randomly drawn from population can be expected to VARY from the population mean as a result of SAMPLING ERROR
2) sampling error (random error)
3) population SD divided by square root of sample size
1) the smaller the sample size, the smaller/larger? the standard error of the mean
2) sampling distribution of mean approaches a normal distribution as what changes
1) larger
2) sample SIZE
(NOT the # of samples)
Acc to null hypothesis, any observed difference between sample mean and population mean is due to ___
sampling (random) error
1) what is an alternative hypothesis
2) what are the types
1) the opposite of the null; predicts that there IS a relationship btwn IV and DV
2) nondirectional (two-tailed) - merely states null is false
directional (one-tailed) - not only states null is false but ALSO predicts direction
1) the size of the rejection region is defined by ___
2) how is this determined
3) when results are "statistically significant," in which region does the obtained statistic fall
1) alpha (level of significance)
2) set by experimenter PRIOR to collecting or analyzing data
3) rejection -- reject the NULL
what determines whether to use a one or two-tailed test
the alternative hypothesis

if it is nondirection, use a two-tailed
if it is directional, use a one-tailed
alpha
1) more likely to make type I error when alpha is small/large?
2) power is increased (more likely to reject false null) when alpha is small/large?
3) more likely to make a Type II error when alpha is small/large?
1) large
2) small
3) small
sample size
1) more likely to make Type I errors when sample size is small/large?
2) power is increased (more likely to reject false null) when sample size is small/large?
3) more likely to make Type II errors when sample size is small/lar
1) small
2) large
3) small

(Type I and II are both more likely when sample size is small)
1) describe a Type I error
2) what is it equal to
3) describe a Type II error
4) what is it equal to
5) describe power
6) what is it equal to
1) reject a true null
2) alpha
3) retain a false null
4) beta
5) reject false null
6) one minus beta
What type of relationship exists between Type I and Type II errors
inverse

as probability of making Type I error increases, probability of making Type II error decreases (and vice versa)
ways to maximize power:
1) increase/decrease alpha
2) increase/decrease sample size
3) increase/decrease effect size -- how?
4) minimize ___
5) use a one/two tailed test
6) use a parametric/non-parametric test
1) increase (more likely to reject null when alpha is .05 than .01)
2) increase (more likely when sample size is 50 rather than 25)
3) increase (maximizing effects of IV increase likelihood that effects will be detected) Effect size is increased by administering IV for long enough and at sufficient intensity
4) error
5) one-tailed
6) parametric
1) what is confidence
2) confidence is maximized when alpha is small/large
2) small
low power means an increase probability of __
retaining a false null
selection of an inferential statistical test is based on:
1) measurement scale of IV/DV
2) what other factor
1) DV
2) design of study
what two assumptions do the parametric and non-parametric tests share
1) sample has been randomly selected from population
2) observations are independent (subject's performance on DV is NOT affected by performance of any other subject)
parametric tests
1) variables are measured on what scales
2) what two assumptions about population distributions must be met
3) violations of these assumptions can increase probability of what type of error
4) how can you describe par
1) interval or ratio
2) a) value of interest is normally distributed in the population
b) when a study includes more than one group, there is homoscedasticity
3) both Type I and II
4) parametric tests are robust - some deviation will not necessarily invalidate results
What is homoscedasticity
variances of the populations that the different groups represent are equal
How do you maximize robustness of a parametric test with regard to:
1) # subjects in groups
2) sample size
3) alpha
1) equal # of subjects in each group
2) large sample size
3) low alpha (e.g., .01)
if scores violate one or both assumptions of parametric tests, what can you do to data to analyze
convert to rank and analyze with non-parametric test
non-parametric tests
1) used to analyze data measured on what scales
2) what types of assumptions are associated with these tests
3) what do they assume about distributions
4) these tests are used to evaluate hypotheses about which as
1) nominal and ordinal
2) none
3) they are distribution-free tests
4) shape
what is the shortcoming of the non-parametric test
less powerful
(less likely to reject a false null)
1) what are degrees of freedom
2) what aspect of the distribution does it determine
1) number of values in a distribution that are "free to vary" given that certain values are known or fixed
2) shape
1) what are the degrees of freedom for a t-test?
2) for a chi-square test?
1) (N-1) total # subject minus one
2) (C-1) total # of categories minus one
1) which test is used to analyze frequency of observations in each category of nominal variable
2) used to determine if the distribution of ___ is equivalent to the distribution of ___
1) chi-square
2) observed (sample) frequencies; expected frequencies (which are predicted by null, reflects no difference)
For a chi-square test:
1) when counting # of variables, do you consider IV or DV
2) how are the expected frequencies determined
1) does not matter
2) does not matter
which test is known as the "goodness of fit" test
single-sample chi-square
single-sample chi-square
1) how many variables
2) measurement scale
3) df (degrees of freedom)
variables = 1

nominal (frequency) data

df = (C - 1)
C = number of columns (levels of the variable)
multiple-sample chi-square
1) how many variables
2) measurement scale
3) df (degrees of freedom)
variables = 2 or more

nominal (frequency) data

df = (C - 1)(R - 1)
C = # columns; R = # rows
What are the tests for ordinal data
Mann-Whitney U
Wilcoxon Matched-Pairs
Kruskal-Wallis
Mann-Whitney U
1) how many IV's
2) # & type of groups for IV
3) measurement scale
IV = 1; 2 independent groups

DV = 1; rank-ordered data
Wilcoxon Matched-Pairs Signed-Ranks
1) how many IV's
2) # & type of groups for IV
3) measurement scale
IV = 1; 2 correlated (matched) groups

DV = 1; rank-ordered data
Kruskal-Wallis
1) how many IV's
2) # & type of groups for IV
3) measurement scale
IV = 1; 2 or more independent groups

DV = 1; rank-ordered data
If a researcher want to determine if 4 major cities differ in terms of frequency of 5 different crimes:
1) what test should be used
2) what are the df
1) multiple sample chi-square
2) (4 - 1)(5 -1) = 12
1) what does a t-test evaluate
2) selection of a t-test is determined b __
3) conducting more than one t-test would be done if __
4) the probability of what type of error is increased when more than one t-test is done
1) differences between 2 means
2) how the 2 means were obtained
3) the study involved more than 2 means
4) Type I (experimentwise error)
t-test for a single sample
1) group (sample) mean is compared to ___
2) how many IV's
3) # & type of groups for IV
4) measurement scale
5) df
1) a known population mean

IV = 1; single group

DV = 1; interval or ratio data

df = (N - 1)
N = # subjects
t-test for independent samples
1) how many IV's
2) # & type of groups for IV
3) measurement scale
4) df
IV = 1; 2 independent groups

DV = 1; interval or ratio data

df = (N - 2)*
N = TOTAL # of subjects
t-test for correlated samples
1) how many IV's
2) # & type of groups for IV
3) measurement scale
4) df
IV = 1; 2 correlated samples

DV = 1; interval or ratio data

df = (N - 1)*
N = PAIRS of scores
1) which t-test do you use when subjects have been matched
2) what 3 ways can you use to "match" subjects
1) t-test for correlated samples
2) a) subjects are matched on an extraneous variable and members of matched pairs are assigned to a different group
c) compare group to itself (within-subjects design)
1) ANOVA is used to compare __
2) ANOVA helps control __
1) 2 or more means
2) experimentwise error rate (probability of making Type I error)
one-way ANOVA
1) how many IV's
2) # & type of groups for IV
3) measurement scale
IV = 1; 2 or more independent groups

DV = 1; interval or ratio data
1) a one-way ANOVA is essentially interchangeable with what test?
2) but what is the convention for using each of them
1) t-test for independent samples
2) t-test for 2 means; ANOVA for 3 or more means
both the ANOVA and t-test compare means
but the ANOVA also analyzes the ___
variability around means

relative contributions of different factors to the total amount of variability observed in set of scores
1) what is the statistic produced by ANOVA
2) how is it calculated
3) what does the formula translate into in practical terms
1) F-ratio
2) MSB/MSW
MSB = mean square within
MSW = mean square between
3) (treatment + error)/error
1) when F = 1, null is true/false?
2) when F > 1, null is true/false
3) the smaller/larger the F, the more statistically significant
1) true
2) false
3) larger F
1) what does a statistically significant F indicate
2) what does it NOT indicate
3) how is this determined
1) there is some difference btwn groups
2) WHICH of the groups differ
3) post-hoc test - used to identify WHICH group means are statistically significant
1) Scheffe S test and Tukey test are examples of what types of tests?
2) what are they used for
1) post-hoc tests
2) after conducting an ANOVA, used to identify WHICH group means are statistically significant
Factorial ANOVA (two-way, three way)
1) how many IV's
2) # & type of groups for IV
3) measurement scale
IV = 2 or more; independent groups

DV = 1; interval or ratio data
1) In a factorial ANOVA, the F-ratios are obtained for what two things
2) In a two-way ANOVA, how many separate F ratios are calcualted
1) a) main effect of EACH IV
b) interactions

2) 3
1) what ANOVA is used when "blocking" has been employed to control an extraneous variable
2) what does it do with the extraneous variable
3) doing this has what benefit
1) randomized block factorial ANOVA
2) treat it as an IV
3) reduces within-group variability --> thereby INCREASING power
Is power increased by reducing/maximizing within-group variability
reducing
1) which test combines ANOVA with regression analysis
2) what does it remove
3) doing this has what benefit
1) ANCOVA
2) the portion of variabiity in DV due to extraneous variable
3) reduces within-group variability --> thereby, increasing power
An ANCOVA removes the protion of variability in __ due to __
DV; extraneous variable
1) a repeated measures ANOVA is appropriate for what type of design
2) specifically for a design in which different level of the __ are __ administered to each subject
1) within-subjects design

2) IV; sequentially
mixed (split-plot) ANOVA
1) how many IV's
2) # & type of groups for IV
3) measurement scale
IV = 2 or more; at least 1 is within-subjects and 1 is between-groups

DV = 1; interval or ratio data
1) similarity in # variables between factorial ANOVA and mixed ANOVA
2) difference
1) both have 2 or more IV's
2) mixed ANOVA is used when at least one IV is btwn-groups and one IV is within-subjects
Trend analysis
1) used when study involves one or more __ IV's
2) researcher wants to evaluate ___
3) results indicate whether or not there is ___
1) quantitative
2) shape or form of the relationship btwn IV and DV's
3) a statistically significant linear or nonlinear trend
MANOVA
1) how many IV's
2) measurement scale
IV = 1 or more

DV = 2 or more; interval or ratio data
1) MANOVA helps control __
2) helps increase ___
3) how?
1) experimentwise error rate (Type I error probability)
2) power
3) increases power by simultaneously assessing effects of the IV on all of the DVs
parametric and nonparametric trests share in common what assumption about samples
random SELECTION of sample from the population
(NOT random assignment)

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