Chapter 2 Flashcards
(25 cards)
α-level
the probability of making a Type I error (usually this value is .05).
β-level
the probability of making a Type II error (Cohen, 1992, suggests a maximum value of 0.2).
Central limit theorem
this theorem states that when samples are large (above about 30) the sampling distribution will take the shape of a normal distribution regardless of the shape of the population from which the sample was drawn. For small samples the t-distribution better approximates the shape of the sampling distribution. We also know from this theorem that the standard deviation of the sampling distribution
Confidence interval
for a given statistic calculated for a sample of observations (e.g. the mean), the confidence interval is a range of values around that statistic that are believed to contain, with a certain probability (e.g. 95%), the true value of that statistic (i.e. the population value)
Degrees of freedom
an impossible thing to define in a few pages let alone a few lines. Essentially it is the number of ‘entities’ that are free to vary when estimating some kind of statistical parameter. In a more practical sense, it has a bearing on significance tests for many commonly used test statistics (such as the F-ratio, t-test, chi-square statistic) and determines the exact form of the probability distribution for
Deviance
the difference between the observed value of a variable and the value of that variable predicted by a statistical model.
Effect size
an objective and (usually) standardized measure of the magnitude of an observed effect. Measures include Cohen’s d, Glass’ g and Pearson’s correlations coefficient, r.
Fit
how sexually attractive you find a statistical test. Alternatively, it’s the degree to which a statistical model is an accurate representation of some observed data. (Incidentally, it’s just plain wrong to find statistical tests sexually attractive.)
Linear model
a model that is based upon a straight line.
Meta-analysis
this is a statistical procedure for assimilating research findings. It is based on the simple idea that we can take effect sizes from individual studies that research the same question, quantify the observed effect in a standard way (using effect sizes) and then combine these effects to get a more accurate idea of the true effect in the population.
One-tailed test
a test of a directional hypothesis. For example, the hypothesis ‘the longer I write this glossary, the more I want to place my editor’s genitals in a starved crocodile’s mouth’ requires a one-tailed test because I’ve stated the direction of the relationship (see also two-tailed test).
Population
in statistical terms this usually refers to the collection of units (be they people, plankton, plants, cities, suicidal authors, etc.) to which we want to generalize a set of findings or a statistical model.
Power
the ability of a test to detect an effect of a particular size (a value of .8 is a good level to aim for).
Sample
a smaller (but hopefully representative) collection of units from a population used to determine truths about that population (e.g. how a given population behaves in certain conditions).
Sampling distribution
the probability distribution of a statistic. We can think of this as follows: if we take a sample from a population and calculate some statistic (e.g. the mean), the value of this statistic will depend somewhat on the sample we took. As such the statistic will vary slightly from sample to sample. If, hypothetically, we took lots and lots of samples from the population and calculated the statistic of
Sampling variation
the extent to which a statistic (e.g. the mean, median, t, F, etc.) varies in samples taken from the same population.
Standard deviation
an estimate of the average variability (spread) of a set of data measured in the same units of measurement as the original data. It is the square root of the variance.
Standard error
the standard deviation of the sampling distribution of a statistic. For a given statistic (e.g. the mean) it tells us how much variability there is in this statistic across samples from the same population. Large values, therefore, indicate that a statistic from a given sample may not be an accurate reflection of the population from which the sample came.
Standard error of the mean (SE)
the full name of the standard error.
Sum of squared errors (SS)
another name for the
Test statistic
a statistic for which we know how frequently different values occur. The observed value of such a statistic is typically used to test hypotheses.
Two-tailed test
a test of a non-directional hypothesis. For example, the hypothesis ‘writing this glossary has some effect on what I want to do with my editor’s genitals’ requires a two-tailed test because it doesn’t suggest the direction of the relationship. (See also One-tailed test.)
Type I error
occurs when we believe that there is a genuine effect in our population, when in fact there isn’t.
Type II error
occurs when we believe that there is no effect in the population when, in reality, there is.
