Statistics and Research Design
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- What type of research design can control for pretest sensitization?
- Solomon 4-groups Design
- Define Solomon 4-group design?
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The Solomon Four-Group Design is designed to deal with a potential testing threat. Recall that a testing threat occurs when the act of taking a test affects how people score on a retest or posttest. The design notation is shown in the figure. It's probably not a big surprise that this design has four groups. Note that two of the groups receive the treatment and two do not. Further, two of the groups receive a pretest and two do not. One way to view this is as a 2x2 (Treatment Group X Measurement Group) factorial design. Within each treatment condition we have a group that is pretested and one that is not. By explicitly including testing as a factor in the design, we are able to assess experimentally whether a testing threat is operating.
Pretest is treated as an additional independent variable. - What is autocorrelation?
- subject's performance on the post-tests is likely to correlate with their performance on the pretests
- What is a disadvantage of the time-series and within-subjects designs?
- they can be confounded by autocorrelation which can decrease power and inflate chances of making a Type I error
- What is Latin Square Design?
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one type of counterbalanced design that involves administering each level of the IV so that it appears the same number of times in each position.
Can help controle multiple treatment interference (order effects, carryover effects). - What is a factorial design?
- whenever a study includes two or more independent variables?
- What type of design combines between-groups and within subjects methodologies?
- mixed (split-plot) design
- What is the multiple baseline design?
- involves sequentially applying the treatment either to different behaviors of the same subject or to the same subject in different settings, or to the same behavior of different subjects. Once the treatment has been applied, it is not withdrawn during the course of the study.
- What type of research designs are used primarily in applied behavioral analysis?
- single-subject designs
- What type of distribution-mean is greater than the median which is greater than the mode?
- postively skewed distribution
- What type of distribution-mean is less than the median, which is less than the mode?
- negatively skewed distribution
- variance VS standard deviation?
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Variance--mean square, measure of variability
SS/(N-1)
the degree to which the scores are dispersed around the distribution's mean
Standard deviation--expressed in same unit of measurement, square root of variance, can be interpreted as a measure of dispersion of scores around the mean - What are the areas under the normal curve?
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+1 to -1 = 68.26%
+2 to -2 = 95.44%
+3 to -3 = 99.72% - Which measure of central tendency is least susceptible to sampling fluctuations?
- mean
- Which measure of central tendency is an unbiased estimate of the population mean?
- mean of a sample that has been randomly slelected from the population
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what kind of distribution when scores are fairly evenly distributed throughout the range of possible scores?
mesokurtic
platykurtic
leptokurtic - platykurtic
- Which measure of central tendency is most useful for open-ended distributions?
- median
- what is affected by adding/substracting a constant to every score in distribution?
- change in measures of central tendency but not variability
- what is affected when each score in distribution is multiplied/divided by constant?
- measures of central tendency and variability
- What is the Central Limit Theorem used for?
- to make predictions of the characteristics of a sampling distribution of the mean
- What are the 3 predictions of the Central Limit Theorem?
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1)as sample size increases, the sampling distribution of the mean approaches a normal distribution
2)mean of the sampling distribution of the mean is equal to the population mean
3)st. dev. of the sampling distribution of the mean is equal to the population st. dev. divided by the square root of the sample size (standard error of the mean) - What is the standard error of the mean?
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st. dev. of a sampling distribution
an estimate of the extent to which the mean of any one sample randomly drawn from a population can be expected to vary from the population as a result of sampling error
measure of variability due to the effects of random error - What affects the size of the standard error of the mean?
- the larger the population st. dev. and the smaller the sample size, the larger the st. error and vice versa
- What is the formula for standard error of the mean?
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SD (of pop)
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√N - According to Central Limit Theorem, the shape of the sampling distribution of means:
- Regardless of the shape of the distribution of individual scores in the population, as the sample size increases the sampling distribution of the mean of the mean approaches a normal distribution.
- what type of research design helps overcome carryover effects?
- counterbalancing
- how to calculate df for single sample chi-square test?
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c-1
where c = number of columns - how to calculate df for multiple sample chi-square?
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(c-1)(r-1)
where c = number of columns and r = number of rows - how to calculate df for single sample t-test?
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n-1
where n = number of subjects - how to calculate df for independent samples?
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n-2
where n = total number of subjects - how to calculate df for t-test correlated samples?
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n-1
where n = number of pairs of scores - how to calculate df for one-way ANOVA?
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(c-1)
(n-c)
where c = number of levels of IV
and n = number of subjects - in ANOVA-df for mean squares between?
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c-1
where c = number of levels of IV - in ANOVA df for TOTAL?
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n - 1
where n = total number of subjects - When deciding on tests for ordinal data, what test to use with two independent groups?
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Mann-Whitney U Test
similar to the t-test for independent samples - With ordinal data, when do you use the Wilcoxin Matched-Pairs Signed-Ranks Test?
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when the study includes two correlated (matched) groups and the differences between the dependent variable scores of subjects who have been matched in pairs are converted to ranks
two correlated groups
similar to the t-test for correlated samples - What test to use with ordinal data and two or more independent groups?
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Kruskal-Wallis Test
similar to the one-way ANOVA - what are the assumptions for inferential statistics?
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data is normally distributed
homoscedasticity-variances of the populations that the different groups represent are equal - what assumption do both parametric and nonparametric prefer?
- random selection from the population
- When is it appropriate to use parametric tests?
- interval or ratio data
- When is it appropriate to use nonparametric data?
- nominal or ordinal data
- How do you maximize the robustness of a parametric test?
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have equal number of subjects in each group (most effective)
large sample size
alpha set to a lower level - When do you use a repeated measures ANOVA?
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2 or more correlated groups
within subjects design - when do you used a mixed or split-plot ANOVA?
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2 or more independent and correlated groups
mixed design - when do you used a randomized block ANOVA?
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when blocking has been used to control an extraneous variable-extraneous variable is treated as an independent variable so that its main and interaction effects can be analyzed
helps reduce within-group variability and increases power - when do you used a MANOVA?
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2 or more dependent variables and one or more independent variable
Allows Experimenter to simultaneously assess the effects of the independent variables on all of the dependent variables.
helps increase power - When do you use ANCOVA?
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allows for control of extraneous variable by removing the portion of variability in the dependent variable due to the extraneous variable
reduces within group variability and increases power
ANOVA with regression analysis - which correlation coefficient do you use with interval or ratio data?
- pearson-product moment
- which correlation coefficient do you use with rank-ordered (ordinal) data?
- Spearman Rank-Order
- Which correlation coefficient do you use with a true dichotomy?
- Phi
- Which correlation coefficient do you use with one dichotomous variable and one interval/ratio variable?
- point-biserial
- which correlation coefficient do you use to assess non-linear relationships?
- Eta
- which correlation coefficient do you use with one artificial dichotomy variable and one interval/ratio variable?
- biserial
- which correlation coefficient do you use with nominal data?
- contingency
- what are the 3 assumptions for correlation coefficients?
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linearity between variables
unrestricted range
homoscedascity - What happens to the correlation coefficient if there is a restriction in range?
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tends to produce a low correlation coefficient and underestimates the true relationship
can threaten a study's internal validity - What is homoscedascity?
- the range of Y scores is about the same for all values of X
- what is the least squares criterion?
- locates the regression line so that the amount of error in prediction is minimized
- what is multi-colinearity?
- a high correlation between predictors
- Why is multi-colinearity undesirable?
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predictors then provide redundant information
magnitude of the regression coefficient is not proportional to the correlation between the predictor and the criterion makding it difficult to predict the regression coefficient - what is the output of multiple regression analysis?
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multiple correlation coefficient
multiple regression equation - What is the multiple correlation coefficient?
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correlation between the criterion and a linear combination of the predictors
R - What is the coefficient of multiple determination?
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R-squared
measure of shared variability - What is the purpose of simultaneous (simple) regression?
- to analyze the effects of all of the predictors on the criterion at once
- What is the purpose of stepwise regression?
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to explain the greatest amount of variability using the fewest possible number of predictors
decision to add or subtract a predictor is based on the resulting change in R-squared - What is forward (stepup) in stepwise regression?
- one predictor is added in each subsequent analysis
- What is backward (step down) in stepwise regression?
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begins with all predictors
one is removed in each subsequent analysis - What is the purpose of hierarchical regression?
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involves several separate analyses
initially-include one or more predictors
subsequent-adding different preditors to the original ones with the selection of predictors based on a well-developed theory or model - what is cross-validation in correlation and prediction?
- whenever a multiple correlation coeffecient and multiple regression equation are tried out on another sample
- why does shrinkage occur in cross-validation of regression?
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because the regression weights were derived from the original sample and do not fit the new sample as well
shrinkage is greatest when the original sample was small and the number of predictors is large - when do you use canonical correlation?
- when two or more continuous predictors are used to predict the status on two or more continuous criteria
- when is it appropriate to use discriminant function analysis?
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when two or more continuous predictors will be used to predict or estimate a person's status on a single discrete criterion
requires the relationships between variables to be linear - when is it appropriate to use logistic regression?
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similar to discriminant function analysis-predict status on a single discrete criterion using two or more continuous or discrete predictors
assumes the relationships between variables are nonlinear - how do you calculate the F-ratio?
- MSB/MSW = (treatment + error)/error
- How do you calculate MST, MSB, MSW?
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MST = SST/df
MSB = SSB/df
MSW = SSW/df
SST = SSB + SSW - What is an interaction effect?
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an effect that occurs when the impact of one independent variable differs at different levels of another variable.
when a study has a significant interaction, the main effects should be interpreted with caution - what is interval recording?
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a method of behavioral sampling that involves dividing a period of time into discrete intervals and recording whether the behavior occurs in each interval
useful for behaviors that have no beginning or end - what is a counterbalanced design?
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research design used to control carryover effects
involves administering the different levels of the IV to different subjects or groups of subjects in a different order
Latin square design is one type - what is a cross-sequential design?
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studies conducted to assess the effects of aging and/or developmental changes over time
help overcome the shortcomings of cross-sectional and longitudinal research by combining the two methodologies - what are single-subject designs?
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research designs originally developed for assessing the effects of an IV on one subject or a few subjects.
characterized by the inclusion of at least one baseline and one treatment phase and by the measurement of the DV at regular intervals during each phase (to control maturation)
AB, ABA, ABAB, multiple-baseline design - why is statistical regression a threat to internal validity?
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tendency of extreme scores on a measure to regress toward the mean when is measure is readministered to the same group of people
problem whenever subjects have been selected because of their extreme status on the dependent variable - why is selection a threat to internal validity?
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threat whenever the method used to assign subjects to treatment groups results in systematic differences between the groups at the beginning of the study
problem when intact groups are used
controlled by randomly assigning subjects to groups or administering a pretest to subjects to determine if the groups differ initially with regard to DV - What are the steps in program evaluation?
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1. specifying the program's goals
2. defining the relevant parameters
3. specifying the techniques and procedures to be used to achieve the program's objectives and goals
4. collecting the relvant data - What is cluster sampling?
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slecting units or groups of individuals from the population
useful when it is not possible to identify or obtain access to the entire population of interest - What is alpha?
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the size of the rejection region or the level of significance
the probability of making a type I error
increased when the sample size is small and when observations are dependent - What is beta?
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the probability of making a type II error
more likely when alpha is low, when the sample size is small, and when independent variable is not administered in sufficient intensity - what is the relationship between alpha and beta?
- inverse relationship