# Key Terms List

α

the probability of making a Type I error; used as shorthand for significance level

β

the probability of making a Type II error; the antithesis of power

Σ

in summation notation, a symbol that denotes “taking the sum” of a series of numbers

Analysis of Variance

also called ANOVA, a system of data analysis that is very flexible and adaptable to a variety of research designs. It is based on a statistical concept called the general linear model and involves the technique of partitioning variance.

bimodal

a descriptor of a distribution indicating that there are two peaks, or two collections of scores

Bonferroni correction

adjustment to avoid inflation of experimentwise risk of Type I error, by dividing significance level by the number of planned contrasts to be conducted

central limit theorem

mathematical theorem that proposes the following: as long as we take a decent-sized sample, if we took many samples (10,000) of large enough size (30+) and took the mean each time, the distribution of those means will approach a normal distribution, even if the scores from each sample are not normally distributed

central tendency

a statistical measure that defines the centre of a distribution with a single score

Cohen’s d

a measure of effect size commonly used to quantify the difference between two population means; 0.2 is small, 0.5 is medium, and 0.8 is considered large

confidence intervals

an approach to inferential statistics that serves as an alternative to hypothesis testing. A statement of where a research population mean should lie with a particular probability.

correlation

statistical analysis of the direction and strength of the relationships between two numerical variables

covariance

the variability that two numeric variables have in common

cutoff sample score

critical value that serves as a decision criterion in hypothesis testing

degrees of freedom

the number of scores in a given calculation that are free to vary.

dependent means t-test

a test for statistical significance when comparing mean difference scores to zero in repeated measures or matched pairs designs

dependent variables

a variable you measure to detect a difference/change as a result of the manipulation -- most often it is numeric

descriptive

ways to summarize or organize data from a research study – essentially allowing us to describe what the data are

directional hypothesis

a research prediction that the research population mean will be “greater than” or "less than" the comparison population mean

distribution of means

also called a sampling distribution, is the distribution of many sample means drawn from the population of individual scores

do not reject the null hypothesis

a decision in hypothesis testing that is inconclusive because the sample score is less extreme than the cutoff score

effect size

a measure of how well a statistical model explains variability, apart from statistical significance, e.g. how big a difference between means is, or just how much variability a regression model explains

experimentwise alpha level

the problem of accumulating risk of Type I error with multiple statistical tests on the same data

factor

in ANOVA, a grouping variable used to account for variance among scores; in an experiment a factor is an independent variable

frequency tables

a way to summarize a dataset in table form, to organize the data and make it easy to get an overview of the dataset quickly

general linear model

an extension of the statistical technique linear regression that is adaptable to various combinations of independent (nominal) and dependent (numeric) variables

grouped frequency table

a frequency table that defines ranges of values in the first column, and reports the frequency of scores that fall within each range

histogram

a graph for summarizing numeric data that essentially is a frequency table that has been turned on its side, with the added benefit of a visual representation of the frequency as the height of the bars in the graph, rather than just a number

homoscedasticity assumption

independent means t-tests require the assumption that the two populations we are comparing have the same variance

hypothesis testing

a formal decision making procedure often used in inferential statistics

independent means t-test

a statistical test used in hypothesis tests comparing the means of two independent samples, created by random assignment of individuals to experimental and control groups

independent variables

a variable you manipulate -- most often it is categorical, or nominal

inferential

analytical tools that allow us to draw conclusions based on data from a research study -- essentially allowing us to make a statement about what the data mean

interaction

the degree to which the contribution of one factor to explaining variability in the data depends on the other factor; the synergy among factors in explaining variance

left skewed

a descriptor of a distribution that indicates asymmetry, specifically with a low frequency tail leading off to the left

levels

the individual conditions or values that make up a factor, a nominal variable that forms the groups in analysis of variance

levels of statistical significance

the probability level that we are willing to accept as a risk that the score from our research sample might occur by random chance within the comparison distribution. By convention, it is set to one of three levels: 10%, 5%, or 1%.

M

the symbol for the mean (average) of scores in a sample

main effect

the degree to which one of the factors explains variability in the data when taken on its own, independent of the other factor

matched pairs

a research design for which a dependent means t-test may be used to test for a hypothesis test; in this design two separate samples are used, but each individual in a sample is matched one-to-one with an individual in the other sample, most often matching participants on a a possible confounding variable as a way to control for the effects of that variable

mean

the same thing as an average: you add up all the numbers, then divide by how many numbers there were. Conceptually we can think of the mean as the balancing point for the distribution.

median

the midpoint of the scores after placing them in order. The median is a counting-based measure: the point at which half of the scores fall above and half of the scores fall below.

mode

the score(s) that occur(s) most often in the dataset

N

the symbol for the number of scores in a sample

nominal

variables that label or categorize something, and any numbers used to measure these variables are arbitrary and do not indicate quantity or size

non-directional hypothesis

a research prediction that the research population mean will be “different from" the comparison population mean, but allows for the possibility that the research population mean may be either greater than or less than the comparison population mean

normal curve

a theoretical distribution, sometimes called a Z distribution, has a very distinct set of properties that make it a useful model for data analysis (e.g. 2-14-34% area rule)

normal curve assumption

parametric tests like the t-test and Z-test require the assumption that the distribution of means for any given population is normally distributed

null hypothesis

the prediction that the population from which sample came is not different from the comparison population

numeric

variables for which numbers are actually meaningful -- they indicate the size or amount of something

one-tailed test

a hypothesis test in which there is only one cutoff sample score on either the lower or the upper end of the comparison distribution

p-value

the probability of the observed sample score or more extreme occurring at random under the comparison distribution

participant variables

variables used like independent variables in (quasi-)experimental research designs, but which cannot be manipulated or assigned randomly to participants, and as such must not generate cause-effect conclusions

partitioning variance

the allocation of variability among scores in numeric data into different buckets, like treatment effects vs. error, or between-groups vs. within-groups variance

percentile

the score at which a given percentage of scores in the normal distribution fall beneath

planned contrasts

statistical tests of pairwise comparisons among groups, used to follow up on a significant ANOVA result, when researchers know in advance which groups they expect to differ

population

all possible individuals or scores about which we would ideally draw conclusions

posthoc tests

statistical tests of pairwise comparisons among groups, used to follow up on a significant ANOVA result, when researchers do not know in advance which groups they expect to differ and wish to test all possible combinations

power

the probability of rejecting the null hypothesis (i.e. finding statistical significance) if the research hypothesis is in fact true. Depends on effect size and sample size.

probability

in a situation where several different outcomes are possible, the probability of any specific outcome is a fraction or proportion of all possible outcomes

r

correlation coefficient that describes the strength and direction of the relationship between two numeric variables. Can be between -1 and 0 and between 0 and +1.

r squared

proportion of variability in one variable that can be explained by the relationship with the other variable. Can be between 0 and 1.

regression

a statistical model that allows for prediction based on a trend line that “best fits” the data points that we have collected. Mathematically, a regression line is one that minimizes the squared deviations (i.e. error) of each point from the line.

reject the null hypothesis

a decision in hypothesis testing that concludes statistical significance because the sample score is more extreme than the cutoff score

repeated measures

also known as within-subjects designs or pre-test post-test design, in which the experiment involves obtaining two separate scores for each individual in a single sample. The same participants are used in all treatment conditions.

research hypothesis

prediction that the population from which the research sample came is different from the comparison population

right skewed

a descriptor of a distribution that indicates asymmetry, specifically with a low frequency tail leading off to the right

sample

the individuals or scores about which we are actually drawing conclusions

Scheffe’s correction

in posthoc analyses, an adjustment to correct for inflated experimentwise risk of Type I error, by dividing the F value by the overall degrees of freedom between from the original overall ANOVA analysis

score

a particular individual’s value on the variable

standard deviation

a common measure of variability in numeric data. The average distance of a scores from the mean.

standard error of the mean

standard deviation of the distribution of means

statistically significant

the conclusion from a hypothesis test that probability of the observed result occurring randomly within the comparison distribution is less than the significance level

Sum of Squares

the sum of squared deviations, or differences, between scores and the mean in a numeric dataset

t-distributions

a series of distributions, based on the normal distribution, that adjust their shape according to degrees of freedom (which in turn is based on sample size)

t-test

statistical test to test the differences between two population means. Suitable for single sample design when standard deviation is unknown, or in two-sample designs.

two-tailed test

a hypothesis test in which there are two cutoff sample scores, one on either end of the comparison distribution

Type I error

if we made the decision to reject the null hypothesis when it is true

Type II error

if we made the decision to not reject the null hypothesis but the research hypothesis is true

μM

population mean for the distribution of means

unimodal

a descriptor of a distribution indicating that there is one peak, or a single collection of scores

value

any possible number or category that a variable could take on

variable

a quality or a quantity that is different for different individuals

variance

a common measure of variability in numeric data. The average squared distance of scores from the mean.

Z-scores

standard scores that allow us to transform scores in any numeric dataset, using any scale, into a standard metric

Z-test

statistical hypothesis test suitable for comparing the means of two populations, when the comparison population mean and standard deviation are known 