EPPP Research / Statistics

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Def: cluster analysis *: Random selection of naturally occurring groups, rather than individuals
Def: analog study: Assessing a phenomenon under conditions that resemble the phenomenon in the field
Def: a cross-sequential research design: A combination of longitudinal and cross-sectional designs

Subjects divided into age groups
Assessed on dependent variable repeatedly over time
Developmental research designs: Longitudinal
Cross-sectional
Cross-sequential
Describe a matching design: Grouping subjects similar on an extraneous variable and then assigning members of the group to each treatment condition
Describe stratified random sampling: Random sampling of sub-groups of a population

eg children, teens, young adults, etc
Describe multiple baseline study *: Single subject
Application of treatment across different baselines (behaviors, settings, individuals)
Used when reversal is not possible or is unethical
Describe a one-group time-series design: Multiple pre-tests, followed by treatment, followed by multiple post-tests

Controls for maturation, testing and regression effects

Vulnerable to history, or a simultaneously occurring event
Formula: variance (s squared): (sum of (X - mean)squared) / n

population denominator n
sample denominator n-1
Formula: z score: (X - mean) / standard deviation
T score attributes: mean = 50
sd = 10
Stanine attributes: Divides score range into equal ninths
Mean = 5
SD = 2
Formula: standard error of the mean *: SE = standard deviation / square root of N

also is SD of the sampling distribution of means

the expected difference between the sample mean and the population mean
Chi square requirements *: Independent observations
Mutually exclusive categories
Frequency, not percentage data used
Formula: ANOVA mean square: mean square = sum of squares / df
Use: phi coefficient: Two dichotomous variables
Use: point-biserial coefficient *: One interval or ratio variable
One naturally dichotomous variable (2 categories)
Use: biserial coefficient *: One interval or ratio variable
One artifically dichotomous variable (2 categories)
(eg scores above, scores below)
Use: contingency coefficient: Two nominally scaled variables, each with more than 2 categories
Use: canonical correlation: Multiple predictors and
multiple criterion values
Use: Spearman's rho: Both predictor and criterion variables are ranked
Def: coefficient of determination: Pearson r squared
% of variability accounted for in the correlation
In an ANOVA, what does within group variance measure: Random variance
Which has the smallest variance? population samples individual samples mean population samples: Mean population samples
When are non-parametric tests used?: When normality can't be assumed
When homogeneity of variance is compromised, the best way to assure result robustness is...?: To keep sample size equal
Use: eta correlation: With non-linear, continuous variables
Distinguish the use of: t-test, one way ANOVA, factorial ANOVA, MANOVA and ANCOVA *: t-test: pair of means

One way ANOVA:
1 independent variable; 2 groups

Factorial ANOVA:
>1 independent variable
permits analysis of interaction effects

MANOVA
>1 dependent variables
minimizes p(Type I error)

ANCOVA
to control for the presence of an extraneous variable
Def: internal validity: Study that permits the conclusion that there is a causal effect between the independent and dependent variable
Threats to internal validity: History - an external event
Maturation
Test learning
Changes in instrumentation
Statistical regression
Subject characteristics
Systematic differences between stickers and dropouts
Experimenter bias
Methods for controlling threats to internal validity: Randomization
Matching
Blocking
Hold extraneous variables constant
ANCOVA
Def: matching: Grouping subjects by status on extraneous variable and then randomly assigning from within groups
Def: blocking: Treating an extraneous variable like another independent variable
Def: time series design: Multiple pre-tests
Treatment
Multiple post-tests

History is a threat to internal validity
Bias in longitudinal studies: Tendency to underestimate age related change, esp decrements

Drop outs tend to be poorer performers

Practice effects on measures
Bias in cross sectional studies: Over estimation of effects due to aging

Cohort effects
Experience
Def: Type II error (beta) *: retaining a false null hypothesis

failing to detect a true effect
Techniques to increase the validity coefficient: Increase the range of scores
Def: shrinkage *: Occurs when predictors are DEVELOPED on one sample and then VALIDATED on another. The correlation coefficient for the second sample is likely to be lower.
def: power *: ability to detect a treatment effect
p (rejecting a false null hypothesis)
p (not making a type II error)
1 - beta
factors affecting power: sample size - larger
alpha - larger
one tailed test
magnitude of the population difference - larger
assumptions of parametric tests: normal distribution of the dependent variable

homogeneity of variance

independence of observations - most critical
Def: F statistic: In an ANOVA, the ratio of between group variance over within group variance
Common non-parametric tests: Chi-square - frequencies of nominal data

Mann-Whitney U - non-parametric equivalent of a t-test; 2 independent groups - nominal scores

Wilcoxon Matched-Pairs test - non-parametric equivalent of a t-test for correlated scores

Kruskal-Wallis test - non-parametric alternative to a one-way ANOVA
ANOVA post-hoc tests: Scheffe provides greatest protection against a type I error, but increases probability of a type II error

Tukey most appropriate for pairwise comparisons
Calculation of CHI-square expected frequencies: simple case = subjects / cells

complex case = column total * row total / total N
Assumptions of Pearson r: linear relationship between variables

homoscedasticity - equal variability on y throughout the x range

r is highest when using the full range of scores on both variables
Use: discriminant function analysis: scores are combined to determine group assignment

in contrast to multiple regression in which multiple variables are combined to predict a score
Def: differential validity: in discriminant analysis, each predictor has a high correlation with a single category criterion and a low correlation with the other category criteria

IQ has low differential validity
Use: structural equation modeling: testing causal models based on multiple variables
Techniques of structural equation modeling *: Path analysis - one way causal relationship with observed values

LISREL - one or two way causal analysis with both observed and infered variables

helps sort out the contributions of true score and error variance
Use: trend analysis: determination of shape of the relationship between variables: eg linear, quadratic, cubic, quartic...

yield the significance of the trend
Def: sampling distribution: a distribution of the values of a statistic (eg the mean) with each value computed from same-sized samples drawn with replacement from the population

has less variability than the population distribution
Central limit theorem *: 1. As sample size increases the shape of the sampling distribution of means approaches a normal shape - even if the distribution of scores is not normal
2.The mean of the sampling distribution of means is equal to the mean of the population
Rosenthal effect: aka experimenter expectancy effect

unintentional effect experimenter exerts towards making the results come out right
experiment-wise error rate: probability of making at least 1 type I error when multiple comparisons are made in a single experiment
heteroscedasticity: unequal variability of y scores at different values of x
Effect on t test when comparison groups are highly correlated: Within group variability is suppressed, giving an artificially high t value
Threats to external validity *: Interaction between selection and treatment would create problems in generalization
Use: tetrachoric coefficient: 2 artificially dichotomous variables
Use: paired t test: Analysis of means when groups are not independent (eg twin studies or repeated measures)

df = # of pairs - 1
ANOVA vs multiple regression: ANOVA uses categorical independent variables only

Multiple regression can use either categorical or continuous variables

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