Final Exam
Example r = .87, R^2 = .76
76% of the variability in the __ can be predicted from how many advertisements they watched leaves 24% of the variability in purchasing behaviour unexplained
The Pearson correlation coefficient compares the amount of ___
COVARIABILITY between two variables to the amount of separate variability in the 2 variables
Pearson correlation coefficient evaluates two aspects of the relationship between two variables:
Direction: positive (+) or negative (-) Strength/consistency: 0-1
_____ is a Pearson correlation coefficient performed on ranked data
Spearmans rho (Ro)
The standardized covariance is called __
The Pearson correlation coefficient
Non-parametric tests The Mann-Whitney U test uses:
The number of sames (no degrees of freedom) and R
Non-parametric tests The Mann-Whitney U test when there is total separation of group ranks:
U = 0
when parametric assumptions are violated or the data are in the form of ranks we use _____
a non-parametric statistic to measure correlation
Non-parametric tests The Wilcoxon Signed-Rank Test: uses data from:
a repeated-measures design to evaluate the difference between two treatment conditions
Non-parametric tests The Mann-Whitney U test first combine:
all the participants from the two samples and rank order the entire data set
Covariance =
average of the sum of the cross-product deviation scores
Variance =
average of the sum of the squared deviation scores
Relationships do not speak to the issue of ____
causality
Non-parametric tests The Wilcoxon Signed-Rank Test: a treatment effect would cause the scores in one condition to be :
consistently larger than the scores in the other condition
A relationship exists when changes in one variable are accompanied by:
constant & predictable changes in the other variable
Direction of causality:
correlation coefficient says nothing about which variable causes the other variable to change
Kendalls tau provides a better estimate of the ___
correlation in a popn than Spearmans more accurate generalizations can be drawn
Pearson correlation coefficient r =
covariance divided by the standard deviation of each
Non-parametric tests The Wilcoxon Signed-Rank Test: treatment effect-- this would cause scores in one treatment to be consistently larger than scores in the other, which would produce _____
difference scores that tended to be either consistently positive or negative
Covariance informs us about the _______
direction of a relationship between two variables
You can solve the problem of by standardizing covariance by :
dividing by the standard deviation (s) of each variable
Non-parametric tests eliminate the ______
effect of outliers and skewness, but can have LESS statistical power than parametric tests
the simplest way to determine if two variables are related is to ___
examine their variance
Non-parametric tests the ranking process results in:
high scores being represented by large ranks, and low scores being represented by small ranks
The third-variable problem:
in any correlation, causality cannot be assumed because there may be other variables (measured or not) that affect results
Coefficient of determination it is the proportion of variance _____
in one variable that is shared by the other variable
Non-parametric tests The Mann-Whitney U test
is the non-parametric altnerative to the independent samples t-test
Pearson correlation coefficient since r is a standarized value:
it is often used as a measure of effect size
The problem with covariance is that:
its size is determined by the SCALE that the variables are measured on
Non-parametric tests: low scores get :
low ranks and high scores get high ranks
Spearman's correlation coefficient useful for ___
minimizing the effects of extreme scores
Kendall's Tau is a _____
non parametric correlation
Pearson correlation coefficient data must be:
numerical scores from an interval or ratio scale of measurement
Pearson's correlation coefficient is strongly affected by the presence of ___
outliers
The population parameter for r is
p
Bivariate correlation one variable plays the role of the _______ we use what we know about its relationship with the outcome variable to ____
predictor make predictions
Non-parametric tests Calculating effect size:
r = the z score / sq root number of observations
Spearman's correlation coefficient scores in each variable are ___
ranked separately
Non-parametric tests The Wilcoxon Signed-Rank Test: the difference between the two measurements for each individual is ____
recorded as the score for the individual
Non-parametric tests The Wilcoxon Signed-Rank Test: The test statistic (T) is the:
smaller of the two sums of ranks (Sum R)
Non-parametric tests The Wilcoxon Signed-Rank Test: The test requires that the difference scores be rank-ordered:
smallest to largest in terms of their ABSOLUTE MAGNITUDE WITHOUT REGARD FOR SIGN OR DIRECTION
Non-parametric tests the idea is that if there are no differences between groups:
some of the higher ranks and some of the lower ranks will fall into each group
even evaluating r as a measure of effect size is __
somewhat subjective
the interpretation of r becomes more intuitive when we _____
square it to produce what is called the coefficient of determination (R^2)
Bivariate correlation measures ___
strength of relationship between 2 continuous variables
Non-parametric tests if most of the high ranks fall in one group and most of the low ranks fall in the other:
suggests there is a difference between the groups
Variance =
sum(X-M)(X-M) divided by the degrees of freedom
Covariance =
sum(X-Mx)(Y-My) divided by degrees of freedom
Pearsons correlation coefficient assumes _
the 2 variables share a linear relationship with one another - do visual inspection
Non-parametric tests are "assumption-free" that are used when ______
the assumptions of normality and/or homogeneity of variance have been violated
Non-parametric tests The Wilcoxon Signed-Rank Test: is the non-parametric alternative to
the dependent samples t-test
Variance describes the extent that the distribution of scores in a variable varies from
the mean
Non parametric tests: analysis is performed on:
the ranks not the raw scores
Spearman's correlation coefficient measures the consistency of ___
the relationship b/w the 2 ordinal variables (ranked scores)
A correlation measures & decribes _
the relationship between 2 variables
Non-parametric tests overcome the problem of _________ by ranking the data
the shape of the distribution of scores (ie giving the lowest score in the distribution a rank of 1)
Non-parametric tests The Mann-Whitney U test the test statistic for the test is
the smaller of the two Uobtained
Variance & covariance is closely linked to
the sum of squares
Interpreting r in teh context of a relationship can be difficult (ie
the value that literally reflects the extent that the points form a straight line)
covariance tells us how much the scores of 2 variables differ from
their respective means
A negative covariance means:
they are negatively related
A positive covariance means:
they are positively related
Non-parametric tests The Mann-Whitney U test uses data from ______ to evaluate ___
two separate samples difference between two treatment conditions
Pearson correlation coefficient reflects degree that ______
two variables form a linear relationship (extent that data fits a straight line)
Coefficient of determination R^2 is the proportion of variance in the outcome variable that can be predicted from _____
variability in the predictor variable
if two variables are related then as scores vary in one direction around the mean of 1 variable, that scores in other variable should ___
vary around the mean of that variable in more or less the same way
Non-parametric tests The Mann-Whitney U test if the obtained U exceeds the critical value for U:
we fail to reject the null hypothesis
Non-parametric tests The Wilcoxon Signed-Rank Test: is Tobtained is less than or equal to the Tcritical -
we reject Ho
Non-parametric tests The Mann-Whitney U test if the obtained U is less than or equal to the critical value for U:
we reject the null hypothesis
Kendalls Tau should be used when __
you have a small data set with a large number of tied ranks