Discovering Statistics Using IBM SPSS Statistics
EXAM QUESTIONS WITH CORRECT
SOLVED ANSWERS.
−2LL - CORRECT ANSWERS✅✅the log-likelihood multiplied by minus 2. This
version of the likelihood is used in logistic regression.
α-level - CORRECT ANSWERS✅✅the probability of making a Type I error (usually
this value is 0.05).
Adjusted mean - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅a measure of the influence of a
particular case of data. It is the predicted value of a case from a model estimated
without that case included in the data. The value is calculated by re-estimating the
model without the case in question, then using this new model to predict the value of the
excluded case. 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. The difference between the predicted value of a case
from the model when that case was included and the predicted value from the model
when it was excluded is the DFFit.
Adjusted R2 - CORRECT ANSWERS✅✅a measure of the loss of predictive power
or shrinkage in regression. The adjusted R2 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.
AIC (Akaike's information criterion) - CORRECT ANSWERS✅✅a goodness-of-fit
measure that is corrected for model complexity. That just means that it 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) - CORRECT ANSWERS✅✅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. A small value represents a better fit to the data.
Alpha factoring - CORRECT ANSWERS✅✅a method of factor analysis.
,Alternative hypothesis - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅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 resulting ANOVA is
therefore an overall test of whether group means differ.
ANCOVA - CORRECT ANSWERS✅✅acronym for analysis of covariance.
Anderson-Rubin method - CORRECT ANSWERS✅✅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.
ANOVA - CORRECT ANSWERS✅✅acronym for analysis of variance.
AR(1) - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅when the residuals of two observations
in a regression model are correlated.
bi - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅the probability of making a Type II error (Cohen,
1992, suggests a maximum value of 0.2).
Bar chart - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅unsurprisingly, this is a test of
the assumption of sphericity. This test 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). Jeremy Miles, who does a lot of multivariate
stuff, claims he's never ever seen a matrix that reached non-significance using this test
and, come to think of it, I've never seen one either (although I do less multivariate stuff),
so you've got to wonder about its practical utility.
Bayes factor - CORRECT ANSWERS✅✅the ratio of the probability of the observed
data given the alternative hypothesis to the probability of the observed data given the
null hypothesis. Put another way, it is the likelihood of the alternative hypothesis relative
to the null. A Bayes factor of 3, for example, means that the observed data are 3 times
more likely under the alternative hypothesis than under the null hypothesis. A Bayes
factor less than 1 supports the null hypothesis by suggesting that the probability of the
data given the null is higher than the probability of the data given the alternative
hypothesis. Conversely, a Bayes factor greater than 1 suggests that the observed data
are more likely given the alternative hypothesis than the null. Values between 1 and 3
are considered evidence for the alternative hypothesis that is 'barely worth mentioning',
values between 3 and 10 are considered 'substantial evidence' ('having substance'
rather than 'very strong') for the alternative hypothesis, and values greater than 10 are
strong evidence for the alternative hypothesis.
Bayesian statistics - CORRECT ANSWERS✅✅a branch of statistics in which
hypotheses are tested or model parameters are estimated using methods based on
Bayes' theorem.
Bayes' theorem - CORRECT ANSWERS✅✅a mathematical description of the
relationship between the conditional probability of events A and B, p(A|B), their reverse
conditional probability, p(B|A), and individual probabilities of the events, p(A) and p(B).
The theorem states that
Between-groups design - CORRECT ANSWERS✅✅another name for independent
design.
, Between-subjects design - CORRECT ANSWERS✅✅another name for independent
design.
BIC (Schwarz's Bayesian information criterion) - CORRECT ANSWERS✅✅a
goodness-of-fit statistic comparable to the AIC, although it is slightly more conservative
(it corrects more harshly for the number of parameters being estimated). It should be
used when sample sizes are large and the number of parameters is small. 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.
Bimodal - CORRECT ANSWERS✅✅a description of a distribution of observations
that has two modes.
Binary logistic regression - CORRECT ANSWERS✅✅logistic regression in which the
outcome variable has exactly two categories.
Binary variable - CORRECT ANSWERS✅✅a categorical variable that has only two
mutually exclusive categories (e.g., being dead or alive).
Biserial correlation - CORRECT ANSWERS✅✅a standardized measure of the
strength of relationship between two variables when one of the two variables is
dichotomous. The biserial correlation coefficient is used when one variable is a
continuous dichotomy (e.g., has an underlying continuum between the categories).
Bivariate correlation - CORRECT ANSWERS✅✅a correlation between two variables.
Blockwise regression - CORRECT ANSWERS✅✅another name for hierarchical
regression.
Bonferroni correction - CORRECT ANSWERS✅✅a correction applied to the -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. This is a simple but effective correction, but
tends to be too strict when lots of tests are performed.
Bootstrap - CORRECT ANSWERS✅✅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 bootstrap samples. From this, confidence
intervals and significance tests can be computed.
EXAM QUESTIONS WITH CORRECT
SOLVED ANSWERS.
−2LL - CORRECT ANSWERS✅✅the log-likelihood multiplied by minus 2. This
version of the likelihood is used in logistic regression.
α-level - CORRECT ANSWERS✅✅the probability of making a Type I error (usually
this value is 0.05).
Adjusted mean - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅a measure of the influence of a
particular case of data. It is the predicted value of a case from a model estimated
without that case included in the data. The value is calculated by re-estimating the
model without the case in question, then using this new model to predict the value of the
excluded case. 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. The difference between the predicted value of a case
from the model when that case was included and the predicted value from the model
when it was excluded is the DFFit.
Adjusted R2 - CORRECT ANSWERS✅✅a measure of the loss of predictive power
or shrinkage in regression. The adjusted R2 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.
AIC (Akaike's information criterion) - CORRECT ANSWERS✅✅a goodness-of-fit
measure that is corrected for model complexity. That just means that it 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) - CORRECT ANSWERS✅✅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. A small value represents a better fit to the data.
Alpha factoring - CORRECT ANSWERS✅✅a method of factor analysis.
,Alternative hypothesis - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅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 resulting ANOVA is
therefore an overall test of whether group means differ.
ANCOVA - CORRECT ANSWERS✅✅acronym for analysis of covariance.
Anderson-Rubin method - CORRECT ANSWERS✅✅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.
ANOVA - CORRECT ANSWERS✅✅acronym for analysis of variance.
AR(1) - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅when the residuals of two observations
in a regression model are correlated.
bi - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅the probability of making a Type II error (Cohen,
1992, suggests a maximum value of 0.2).
Bar chart - CORRECT ANSWERS✅✅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 - CORRECT ANSWERS✅✅unsurprisingly, this is a test of
the assumption of sphericity. This test 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). Jeremy Miles, who does a lot of multivariate
stuff, claims he's never ever seen a matrix that reached non-significance using this test
and, come to think of it, I've never seen one either (although I do less multivariate stuff),
so you've got to wonder about its practical utility.
Bayes factor - CORRECT ANSWERS✅✅the ratio of the probability of the observed
data given the alternative hypothesis to the probability of the observed data given the
null hypothesis. Put another way, it is the likelihood of the alternative hypothesis relative
to the null. A Bayes factor of 3, for example, means that the observed data are 3 times
more likely under the alternative hypothesis than under the null hypothesis. A Bayes
factor less than 1 supports the null hypothesis by suggesting that the probability of the
data given the null is higher than the probability of the data given the alternative
hypothesis. Conversely, a Bayes factor greater than 1 suggests that the observed data
are more likely given the alternative hypothesis than the null. Values between 1 and 3
are considered evidence for the alternative hypothesis that is 'barely worth mentioning',
values between 3 and 10 are considered 'substantial evidence' ('having substance'
rather than 'very strong') for the alternative hypothesis, and values greater than 10 are
strong evidence for the alternative hypothesis.
Bayesian statistics - CORRECT ANSWERS✅✅a branch of statistics in which
hypotheses are tested or model parameters are estimated using methods based on
Bayes' theorem.
Bayes' theorem - CORRECT ANSWERS✅✅a mathematical description of the
relationship between the conditional probability of events A and B, p(A|B), their reverse
conditional probability, p(B|A), and individual probabilities of the events, p(A) and p(B).
The theorem states that
Between-groups design - CORRECT ANSWERS✅✅another name for independent
design.
, Between-subjects design - CORRECT ANSWERS✅✅another name for independent
design.
BIC (Schwarz's Bayesian information criterion) - CORRECT ANSWERS✅✅a
goodness-of-fit statistic comparable to the AIC, although it is slightly more conservative
(it corrects more harshly for the number of parameters being estimated). It should be
used when sample sizes are large and the number of parameters is small. 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.
Bimodal - CORRECT ANSWERS✅✅a description of a distribution of observations
that has two modes.
Binary logistic regression - CORRECT ANSWERS✅✅logistic regression in which the
outcome variable has exactly two categories.
Binary variable - CORRECT ANSWERS✅✅a categorical variable that has only two
mutually exclusive categories (e.g., being dead or alive).
Biserial correlation - CORRECT ANSWERS✅✅a standardized measure of the
strength of relationship between two variables when one of the two variables is
dichotomous. The biserial correlation coefficient is used when one variable is a
continuous dichotomy (e.g., has an underlying continuum between the categories).
Bivariate correlation - CORRECT ANSWERS✅✅a correlation between two variables.
Blockwise regression - CORRECT ANSWERS✅✅another name for hierarchical
regression.
Bonferroni correction - CORRECT ANSWERS✅✅a correction applied to the -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. This is a simple but effective correction, but
tends to be too strict when lots of tests are performed.
Bootstrap - CORRECT ANSWERS✅✅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 bootstrap samples. From this, confidence
intervals and significance tests can be computed.
