GLOSSARY
Alternative hypothesis: the prediction that
is not tentatively held to be true; it states that a relationship will
be found between two variables, or that the means of multiple groups
are not equal.
Appropriate sample size: Too large a sample tends to yield statistical significance even in the presence of a small effect; i.e., statistical significance overrides the practical significance of your results. Such a situation leads to inflated Type I error. On the other hand, too small a sample size tends to suggest that there is no reasonable effect in your study; but, even a large effect can be difficult to detect if the sample size is inadequate. This situation leads to increased chance of Type II error. An appropriate sample size is one that can detect a statistical difference or effect that you feel represents a meaningful practical result, given that such an effect truly exists within the data, without wastefully oversampling.
Categorical variable: a characteristic that
has been measured on the nominal scale.
Cohen's d: An effect size measure representing the standardized
difference between two means.
Condition (Group) mean: the average of the scores of all individuals
in a group.
Confidence interval: range of values that is formed to contain
within its boundaries, with a predetermined level of confidence, the
population value being estimated.
Continuous variable: a variable that theoretically can assume
an infinite number of values (something that is measurable and ongoing).
Contrast(s): Specific question(s) regarding the differences
between two or more means. A method for comparing two or more means.
Critical value: a value that a statistic must surpass in order
to have a hypothesis test result in rejection of the null hypothesis
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Dependent groups ttest: A statistical technique
to compare the means of two related samples, such as prepost differences,
or analyses comparing the means of dependent pairs such as husbands
and wives, sibling pairs, twins, etc. Also called a paired or correlated
ttest.
Effect size: An index measuring the magnitude
of a specific result. Effect sizes can be standardized comparisons of
means, or they can be correlation coefficients or squared correlation
coefficients. Effect sizes are used to assess the degree to which the
research hypothesis under study is actually observed via the sample
data.
Factorial analysis of variance: a procedure
for comparing the mean scores of two or more groups based on two or
more (categorical) independent variables; it also tests for interactions
among the IVs.
Fdistribution: a theoretical relative frequency distribution
of the ratio of two independent sample variances.
Greek letters and symbols
Independent groups ttest: procedure for comparing
the mean scores of two independent groups on a given quantitative variable.
Multiple regression: a procedure for determining
the relationship between a criterion variable and several predictor
variables
Null hypothesis: the prediction that is tentatively
held to be true; it states that no relationship will be found between
two variables, or that the means of multiple groups are equal.
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Onetailed test: a statistical test in which
the critical region for rejecting the null hypothesis falls in one direction
of the probability distribution
Oneway analysis of variance: a procedure for comparing the
mean scores of two or more groups based on one categorical independent
variable
Paired ttest: procedure for comparing the mean
scores of two variables for each case. Also see dependent groups ttest.
PartialR^{2}: In multiple regression, the partialR^{2}
for X_{p} indicates the strength of the relationship between
an independent variable and the outcome, adjusting or controlling for
the presence of any other previously entered independent variables in
the model. The partialR^{2} for X_{p} represents the
proportion of residual variance explained by the addition of X_{p}.
PartR^{2} (also called semipartialR^{2}):
In a multiple regression model, the semipartial or partR^{2}
for X_{p} represents the proportion of variance of the outcome
that is uniquely attributed to X_{p}, controlling for the contribution
of all other variables in the model.
Pooled variance: Also called "withingroups" variability.
Under the assumption of equal population variances, the pooled variance
represents the best estimate of this equal but unknown population variance.
It is a weighted average of the variance within each group.
Population: The group or collection of individuals from which
a sample was drawn, and/or to which one hopes to generalize based on
sample results.
Power: In hypothesis testing, the power refers to the probability
of making a correct decision to reject the null hypothesis. Power tells
us the likelihood of detecting a difference between groups, or a hypothesized
relationship within the population of interest.
pvalue: obtained significance level for a statistical test.
The pvalue represents the likelihood, under the assumption that the
null hypothesis is true, that the data would yield the obtained results.
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R^{2}: Represents the overall proportion
of variance in an outcome that's accounted for by a (regression) model.
Sample: Collection of observations selected
in a such a way to offer a model of the population of interest.
SemipartialR^{2}: see partR^{2}
Significance level: In hypothesis testing, the significance
level refers to the probability of making a Type I error, or rejecting
the null hypothesis when it is actually true. The researcher decides
on the level of significance for each test.
Standard deviation: For a collection of observations, the standard
deviation (S) represents "average" deviation from the mean.
It is the square root of the variance.
Standard error: In multiple regression, the standard error represents
"average" deviation between actual and predicted observations.
Graphically, it represents the spread or variability around the predication
line. Standard errors are also found for statistics, such as standard
error of the mean, standard error for a proportion, etc. In this context,
the standard error refers to the standard deviation of the sampling
distribution for that statistic.
Standard error of the difference: Refers to the standard deviation
of the sampling distribution for the difference of two means; it is
the denominator used when calculating the observed tstatistic for a
twosample ttest.
tdistribution: a theoretical relative frequency
distribution in which the standard error of the mean is estimated from
sample values. Similar to a normal distribution but used when population
variances are unknown.
Twotailed test: a statistical test in which the critical region
for rejecting the null hypothesis falls in both directions of the probability
distribution.
Variance: The variance (S^{2}) represents
"average" squared deviations from the mean for a set of observations.
Variances may be determined for linear combinations of observations
as well.
Zdistribution: Standard normal distribution.
Theoretical distribution of population scores where the mean always
equals zero and the standard deviation equals one.
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