Statistics and Research Design: Inferential
statistics tests and Correlational Techniques
3 correlation assumptions that must be met: - ANSWER-Linearity
Unrestricted rage
Homoscedasticity
Analysis of Covariance (ANCOVA) - ANSWER-Allows a researcher to control an extraneous variable by
statistically removing the variability in the DV that is due to the extraneous variable
ANOVA - ANSWER-Used to compare means of two or more groups
- helps control experimentwise error rate
Biserial correlation - ANSWER-Coefficient used for evaluating the association between an artificially
made dichotomous variable (yes/no) and one interval/ratio scale variable
Canonical Correlation - ANSWER-An extension of MR
- Used when 2+ predictors are used to predict 2+ criterion
Chi-square test - ANSWER-A nonparametric test used to analyze the frequency of observations in each
level of the variables
- used to determine if distribution of observed (sample) frequencies is equal to dist. of expected
frequencies
- it is a way to compare observed data (what actually happened) to expected data (what we expect to
happen). It is commonly used to test if two categorical variables are related in some way, like voting
behavior and gender, or if the observed data fits a theoretical distribution, like flipping a fair coin.
- do not have to distinguish between IV and DV
Coefficient of Determination (R^2) - ANSWER-It is a correlation coefficient squared
- a measure of the goodness of fit of a model in regression analysis
- measures the proportion of variation in the dependent variable that is explained by the independent
variable in a linear regression analysis, and ranges from 0 to 1.
- Provides a measure of SHARED VARIABILITY between 2 different correlated variables
- Indicates the proportion of of variability in Y that is accounted for by variability in X
Ex: if the correlation coefficient for sales success and product knowledge is .60, then 36% (.60 squared =
.36) of variability in sales success is accounted for by product knowledge. Remaining 64% is due to
unexplained variability
Cohen's d - ANSWER-A measure of effect size that assesses the difference between two group means in
terms of standard deviation
d = .2 is small
, Statistics and Research Design: Inferential
statistics tests and Correlational Techniques
d = .5 is medium
d = .8 is large
Cross-validation - ANSWER-When researcher tries out their correlation coefficient and MR equation on
another sample
- This tends to cause SHRINKAGE in the coefficients and predictive accuracy of regression equation
Data reduction techniques (2): - ANSWER-1. Factor analysis: reducing a large number of variables to
smaller number of factors that explain the intercorrelations between variables
2. Cluster analysis: used to group people/objects into smaller number of mutually exclusive groups
(clusters) based on similarities
- used to identify/confirm the nature and number of distinct groups
Discriminant Function Analysis - ANSWER-Used when 2+ predictors are used to predict a person's status
on a single discrete (nominal) criterion
Eta squared (n^2) - ANSWER-Measure of effect size that indicates the percent of variance in the DV that
is accounted for my variance in the IV (treatment)
Ex: eta squared = .5 means that 50% of the variability is accounted for by the manipulation of the IV
Examples of non-parametric tests (tests that do not make any assumptions about the underlying
probability distribution of the data) - ANSWER-Wilcoxon matched-pairs signed-ranks test
Mann-Whitney U test
Kruskal-Wallis test
Chi-square test
- used when data is likely not normally distributed or when sample size is small
Experimentwise error rate - ANSWER-Refers to the probability of making a Type I error. As the number
of statistical comparisons in a study increases, this rate also increases.
F ratio and formula - ANSWER-A test statistic used in ANOVA
- the ratio between the variability observed between treatment groups and the variability observed
within treatment groups. (bigger = better
Formula:
F = MSB/MSW
statistics tests and Correlational Techniques
3 correlation assumptions that must be met: - ANSWER-Linearity
Unrestricted rage
Homoscedasticity
Analysis of Covariance (ANCOVA) - ANSWER-Allows a researcher to control an extraneous variable by
statistically removing the variability in the DV that is due to the extraneous variable
ANOVA - ANSWER-Used to compare means of two or more groups
- helps control experimentwise error rate
Biserial correlation - ANSWER-Coefficient used for evaluating the association between an artificially
made dichotomous variable (yes/no) and one interval/ratio scale variable
Canonical Correlation - ANSWER-An extension of MR
- Used when 2+ predictors are used to predict 2+ criterion
Chi-square test - ANSWER-A nonparametric test used to analyze the frequency of observations in each
level of the variables
- used to determine if distribution of observed (sample) frequencies is equal to dist. of expected
frequencies
- it is a way to compare observed data (what actually happened) to expected data (what we expect to
happen). It is commonly used to test if two categorical variables are related in some way, like voting
behavior and gender, or if the observed data fits a theoretical distribution, like flipping a fair coin.
- do not have to distinguish between IV and DV
Coefficient of Determination (R^2) - ANSWER-It is a correlation coefficient squared
- a measure of the goodness of fit of a model in regression analysis
- measures the proportion of variation in the dependent variable that is explained by the independent
variable in a linear regression analysis, and ranges from 0 to 1.
- Provides a measure of SHARED VARIABILITY between 2 different correlated variables
- Indicates the proportion of of variability in Y that is accounted for by variability in X
Ex: if the correlation coefficient for sales success and product knowledge is .60, then 36% (.60 squared =
.36) of variability in sales success is accounted for by product knowledge. Remaining 64% is due to
unexplained variability
Cohen's d - ANSWER-A measure of effect size that assesses the difference between two group means in
terms of standard deviation
d = .2 is small
, Statistics and Research Design: Inferential
statistics tests and Correlational Techniques
d = .5 is medium
d = .8 is large
Cross-validation - ANSWER-When researcher tries out their correlation coefficient and MR equation on
another sample
- This tends to cause SHRINKAGE in the coefficients and predictive accuracy of regression equation
Data reduction techniques (2): - ANSWER-1. Factor analysis: reducing a large number of variables to
smaller number of factors that explain the intercorrelations between variables
2. Cluster analysis: used to group people/objects into smaller number of mutually exclusive groups
(clusters) based on similarities
- used to identify/confirm the nature and number of distinct groups
Discriminant Function Analysis - ANSWER-Used when 2+ predictors are used to predict a person's status
on a single discrete (nominal) criterion
Eta squared (n^2) - ANSWER-Measure of effect size that indicates the percent of variance in the DV that
is accounted for my variance in the IV (treatment)
Ex: eta squared = .5 means that 50% of the variability is accounted for by the manipulation of the IV
Examples of non-parametric tests (tests that do not make any assumptions about the underlying
probability distribution of the data) - ANSWER-Wilcoxon matched-pairs signed-ranks test
Mann-Whitney U test
Kruskal-Wallis test
Chi-square test
- used when data is likely not normally distributed or when sample size is small
Experimentwise error rate - ANSWER-Refers to the probability of making a Type I error. As the number
of statistical comparisons in a study increases, this rate also increases.
F ratio and formula - ANSWER-A test statistic used in ANOVA
- the ratio between the variability observed between treatment groups and the variability observed
within treatment groups. (bigger = better
Formula:
F = MSB/MSW
