Discovering Statistics Using IBM SPSS Statistics, 5e REAL
EXAM 400 CORRECT SOLUTIONS
Alternative hypothesis - ANSWER-the prediction that there will be an effect (i.e., that your
experimental manipulation will have some effect or that certain variables will relate to each other).
Analysis of covariance (ANCOVA) - ANSWER-a statistical procedure that uses the F-statistic to test
the overall fit of a linear model, adjusting for the effect that one or more covariates have on the
outcome variable. In experimental research this linear model tends to be defined in terms of group
means and the resulting ANOVA is therefore an overall test of whether group means differ after the
variance in the outcome variable explained by any covariates has been removed.
Analysis of variance (ANOVA) - ANSWER-a statistical procedure that uses the F-statistic to test the
overall fit of a linear model.
In experimental research this linear model tends to be defined in terms of group means, and the
result is therefore an overall test of whether group means differ.
Anderson-Rubin method - ANSWER-a way of calculating factor scores which produces scores that
are uncorrelated and standardized with a mean of 0 and a standard deviation of 1.
AR(1) - ANSWER-this stands for first-order autoregressive structure. It is a covariance structure
used in multilevel linear models in which the relationship between scores changes in a systematic
way. It is assumed that the correlation between scores gets smaller over time and that variances are
assumed to be homogeneous. This structure is often used for repeated-measures data (especially
when measurements are taken over time such as in growth models).
Autocorrelation - ANSWER-when the residuals of two observations in a regression model are
correlated.
bi - ANSWER-unstandardized regression coefficient. Indicates the strength of relationship between
a given predictor, i, of many and an outcome in the units of measurement of the predictor. It is the
change in the outcome associated with a unit change in the predictor.
,βi - ANSWER-standardized regression coefficient. Indicates the strength of relationship between a
given predictor, i, of many and an outcome in a standardized form. It is the change in the outcome (in
standard deviations) associated with a one standard deviation change in the predictor.
β-level - ANSWER-the probability of making a Type II error (Cohen, 1992, suggests a maximum
value of 0.2).
Bar chart - ANSWER-a graph in which a summary statistic (usually the mean) is plotted on the y-
axis against a categorical variable on the x-axis (this categorical variable could represent, for example,
groups of people, different times or different experimental conditions). The value of the mean for
each category is shown by a bar. Different-coloured bars may be used to represent levels of a second
categorical variable.
Bartlett's test of sphericity - ANSWER-A test of the assumption of sphericity that examines
whether a variance-covariance matrix is proportional to an identity matrix
Therefore, it effectively tests whether the diagonal elements of the variance-covariance matrix are
equal (i.e., group variances are the same), and whether the off-diagonal elements are approximately
zero (i.e., the dependent variables are not correlated).
Questionable practical utility because it's often significant
Bimodal - ANSWER-a description of a distribution of observations that has two values that appear
most often
Binary logistic regression - ANSWER-logistic regression in which the outcome variable has exactly
two categories.
Binary variable - ANSWER-a categorical variable that has only two mutually exclusive categories
(e.g., being dead or alive).
Biserial correlation - ANSWER-a standardized measure of the strength of relationship between two
variables when one of the two variables is dichotomous.
Bivariate correlation - ANSWER-a correlation between two variables.
,Blockwise regression - ANSWER-another name for hierarchical regression.
Bonferroni correction - ANSWER-a correction applied to the α-level to control the overall Type I
error rate when multiple significance tests are carried out. Each test conducted should use a criterion
of significance of the α-level (normally 0.05) divided by the number of tests conducted. *Tends to be
too strict when lots of tests are performed*
Bootstrap - ANSWER-a technique from which the sampling distribution of a statistic is estimated
by taking repeated samples (with replacement) from the data set (in effect, treating the data as a
population from which smaller samples are taken). The statistic of interest (e.g., the mean, or b
coefficient) is calculated for each sample, from which the sampling distribution of the statistic is
estimated. The standard error of the statistic is estimated as the standard deviation of the sampling
distribution created from the <___> samples. From this, confidence intervals and significance tests
can be computed.
−2LL - ANSWER-the log-likelihood multiplied by minus 2.
*used in logistic regression*
Biserial correlation coefficient - ANSWER-Coefficient used when one variable is a continuous
dichotomy (e.g., has an underlying continuum between the categories).
α-level - ANSWER-the probability of making a Type I error (usually this value is 0.05).
Adjusted mean - ANSWER-in the context of analysis of covariance this is the value of the group
mean adjusted for the effect of the covariate.
Adjusted predicted value - ANSWER-The predicted value of a case from a model estimated without
that case included in the data, calculated by re-estimating the model without the case in question,
then using this new model to predict the value of the excluded case.
*A measure of the influence of a particular case of data*
How to interpret adjusted predicted value - ANSWER-If a case does not exert a large influence
over the model then its predicted value should be similar regardless of whether the model was
estimated including or excluding that case.
, Adjusted R² - ANSWER-This tells us how much variance in the outcome would be accounted for if
the model had been derived from the population from which the sample was taken.
*measure of the loss of predictive power/shrinkage in regression*
AIC (Akaike's information criterion) - ANSWER-a goodness-of-fit measure that is corrected for
model complexity (takes account of how many parameters have been estimated).
It is not intrinsically interpretable, but can be compared in different models to see how changing the
model affects the fit. A small value represents a better fit to the data.
AICC (Hurvich and Tsai's criterion) - ANSWER-a goodness-of-fit measure that is similar to AIC but is
designed for small samples. It is not intrinsically interpretable, but can be compared in different
models to see how changing the model affects the fit.
Small value=better fit
Alpha factoring - ANSWER-a method of factor analysis.
Boredom effect - ANSWER-refers to the possibility that performance in tasks may be influenced
(the assumption is a negative influence) by ____ or lack of concentration if there are many tasks, or
the task goes on for a long period of time.
Boxplot
AKA
box-whisker diagram - ANSWER-a graphical representation of some important characteristics of a
set of observations. At the centre of the plot is the median, which is surrounded by a box the top and
bottom of which are the limits within which the middle 50% of observations fall (the interquartile
range). Sticking out of the top and bottom of the box are two whiskers which extend to the highest
and lowest extreme scores, respectively.
Box's test - ANSWER-a test of the assumption of homogeneity of covariance matrices. This test
should be non-significant if the matrices are roughly the same.
PROBLEMS: very susceptible to deviations from multivariate normality and so may be non-significant
not because the variance-covariance matrices are similar across groups, but because the assumption
of multivariate normality is not tenable.
EXAM 400 CORRECT SOLUTIONS
Alternative hypothesis - ANSWER-the prediction that there will be an effect (i.e., that your
experimental manipulation will have some effect or that certain variables will relate to each other).
Analysis of covariance (ANCOVA) - ANSWER-a statistical procedure that uses the F-statistic to test
the overall fit of a linear model, adjusting for the effect that one or more covariates have on the
outcome variable. In experimental research this linear model tends to be defined in terms of group
means and the resulting ANOVA is therefore an overall test of whether group means differ after the
variance in the outcome variable explained by any covariates has been removed.
Analysis of variance (ANOVA) - ANSWER-a statistical procedure that uses the F-statistic to test the
overall fit of a linear model.
In experimental research this linear model tends to be defined in terms of group means, and the
result is therefore an overall test of whether group means differ.
Anderson-Rubin method - ANSWER-a way of calculating factor scores which produces scores that
are uncorrelated and standardized with a mean of 0 and a standard deviation of 1.
AR(1) - ANSWER-this stands for first-order autoregressive structure. It is a covariance structure
used in multilevel linear models in which the relationship between scores changes in a systematic
way. It is assumed that the correlation between scores gets smaller over time and that variances are
assumed to be homogeneous. This structure is often used for repeated-measures data (especially
when measurements are taken over time such as in growth models).
Autocorrelation - ANSWER-when the residuals of two observations in a regression model are
correlated.
bi - ANSWER-unstandardized regression coefficient. Indicates the strength of relationship between
a given predictor, i, of many and an outcome in the units of measurement of the predictor. It is the
change in the outcome associated with a unit change in the predictor.
,βi - ANSWER-standardized regression coefficient. Indicates the strength of relationship between a
given predictor, i, of many and an outcome in a standardized form. It is the change in the outcome (in
standard deviations) associated with a one standard deviation change in the predictor.
β-level - ANSWER-the probability of making a Type II error (Cohen, 1992, suggests a maximum
value of 0.2).
Bar chart - ANSWER-a graph in which a summary statistic (usually the mean) is plotted on the y-
axis against a categorical variable on the x-axis (this categorical variable could represent, for example,
groups of people, different times or different experimental conditions). The value of the mean for
each category is shown by a bar. Different-coloured bars may be used to represent levels of a second
categorical variable.
Bartlett's test of sphericity - ANSWER-A test of the assumption of sphericity that examines
whether a variance-covariance matrix is proportional to an identity matrix
Therefore, it effectively tests whether the diagonal elements of the variance-covariance matrix are
equal (i.e., group variances are the same), and whether the off-diagonal elements are approximately
zero (i.e., the dependent variables are not correlated).
Questionable practical utility because it's often significant
Bimodal - ANSWER-a description of a distribution of observations that has two values that appear
most often
Binary logistic regression - ANSWER-logistic regression in which the outcome variable has exactly
two categories.
Binary variable - ANSWER-a categorical variable that has only two mutually exclusive categories
(e.g., being dead or alive).
Biserial correlation - ANSWER-a standardized measure of the strength of relationship between two
variables when one of the two variables is dichotomous.
Bivariate correlation - ANSWER-a correlation between two variables.
,Blockwise regression - ANSWER-another name for hierarchical regression.
Bonferroni correction - ANSWER-a correction applied to the α-level to control the overall Type I
error rate when multiple significance tests are carried out. Each test conducted should use a criterion
of significance of the α-level (normally 0.05) divided by the number of tests conducted. *Tends to be
too strict when lots of tests are performed*
Bootstrap - ANSWER-a technique from which the sampling distribution of a statistic is estimated
by taking repeated samples (with replacement) from the data set (in effect, treating the data as a
population from which smaller samples are taken). The statistic of interest (e.g., the mean, or b
coefficient) is calculated for each sample, from which the sampling distribution of the statistic is
estimated. The standard error of the statistic is estimated as the standard deviation of the sampling
distribution created from the <___> samples. From this, confidence intervals and significance tests
can be computed.
−2LL - ANSWER-the log-likelihood multiplied by minus 2.
*used in logistic regression*
Biserial correlation coefficient - ANSWER-Coefficient used when one variable is a continuous
dichotomy (e.g., has an underlying continuum between the categories).
α-level - ANSWER-the probability of making a Type I error (usually this value is 0.05).
Adjusted mean - ANSWER-in the context of analysis of covariance this is the value of the group
mean adjusted for the effect of the covariate.
Adjusted predicted value - ANSWER-The predicted value of a case from a model estimated without
that case included in the data, calculated by re-estimating the model without the case in question,
then using this new model to predict the value of the excluded case.
*A measure of the influence of a particular case of data*
How to interpret adjusted predicted value - ANSWER-If a case does not exert a large influence
over the model then its predicted value should be similar regardless of whether the model was
estimated including or excluding that case.
, Adjusted R² - ANSWER-This tells us how much variance in the outcome would be accounted for if
the model had been derived from the population from which the sample was taken.
*measure of the loss of predictive power/shrinkage in regression*
AIC (Akaike's information criterion) - ANSWER-a goodness-of-fit measure that is corrected for
model complexity (takes account of how many parameters have been estimated).
It is not intrinsically interpretable, but can be compared in different models to see how changing the
model affects the fit. A small value represents a better fit to the data.
AICC (Hurvich and Tsai's criterion) - ANSWER-a goodness-of-fit measure that is similar to AIC but is
designed for small samples. It is not intrinsically interpretable, but can be compared in different
models to see how changing the model affects the fit.
Small value=better fit
Alpha factoring - ANSWER-a method of factor analysis.
Boredom effect - ANSWER-refers to the possibility that performance in tasks may be influenced
(the assumption is a negative influence) by ____ or lack of concentration if there are many tasks, or
the task goes on for a long period of time.
Boxplot
AKA
box-whisker diagram - ANSWER-a graphical representation of some important characteristics of a
set of observations. At the centre of the plot is the median, which is surrounded by a box the top and
bottom of which are the limits within which the middle 50% of observations fall (the interquartile
range). Sticking out of the top and bottom of the box are two whiskers which extend to the highest
and lowest extreme scores, respectively.
Box's test - ANSWER-a test of the assumption of homogeneity of covariance matrices. This test
should be non-significant if the matrices are roughly the same.
PROBLEMS: very susceptible to deviations from multivariate normality and so may be non-significant
not because the variance-covariance matrices are similar across groups, but because the assumption
of multivariate normality is not tenable.
