PSC third final

alpha level (a)

the value, selected by the researcher, that marks an extreme probability of the null distribution in which scores are less likely to occur by chance; value is also the likelihood of making a Type 1 error

alternative hypothesis

a hypothesis that contradicts the null hypothesis by stating that the population parameter is less than/greater than/equal to the value given in the null hypothesis

ANOVA (analysis of variance)

a statistical procedure in which the variance in data is divided into distinct components: systematic and random variance

bar graph

a graph in which each value of a nominal-level or ordinal-level variable is represented by a bar drawn to a height representative of that value’s frequency in a set of data (or some other dependent variable)

Bayesian inference

a form of reasoning depending on the idea that a probability is a degree of belief, rather than a long-run frequency, such that a prior set of beliefs can be updated by new evidence to create a posterior set of beliefs

between-groups design

a study in which individuals or experimental conditions and each individual provides only one score for data analysis

bimodal

a distribution that included two peaks or modes

bivariate line regression

a regression analysis in which one predictor, or independent, variable (x) is assumed to be related to one criterion, or dependent, variable (y) in such a manner that the direction and rate of change of one variable is constant with the respect to the changes in the other variable

categorial (qualitative) variables

variables that have values that are types, kinds, or categories and that do not have any numeric properties

central tendency

a measure that describes the middle of a distribution; most commonly measured with the mean, median, and mode

chi-square goodness-of-fit

a null hypothesis test that evaluates whether a variable whose values are categorical fits a theoretical distribution

chi-square test of independence

a null hypothesis that evaluates the relationship between two variables whose variables are categorical

Cohen’s d

a form of effect size that measures the distance between two means in standard deviation units

condition (level)

a category or level of a variable whose values are manipulated by a researcher. Study participants are then assigned to receive or be exposed to one or more of the different conditions

confidence interval

an interval centered on a statistical of interest, bounded by lower and upper limits that define a range of values within which a population parameter will lie with a certain confidence level, given as a percent

confidence level

a value expressing the frequency with which a given confidence interval contains the true value of the parameter being estimated

continuous variables

variables with values that can always be further divided and where it is at least theoretically possible to find an observation with a value that will fall between two other variables, no matter how close they are

correlation

a particular quantitative measurement of the direction and strength of the relationship between two or more variables

correlational analysis

a statistical procedure to test whether a correlation coefficient is significantly different from zero, which represents the null hypothesis

correlation coefficient

the sample statistic in a correlational analysis that quantifies the linear relationship between two variables and ranges from -1 to +1

discrete variables

variables represented by whole numbers and for which there are no intermediate values for two values that are adjacent on the scale

descriptive statistics

statistics that summarize a set of data - a measure of central tendency or variability

deviation score

the value obtained when you subtract an observation minus the sample mean

effect size

a quantitative measure of the magnitude of an effect that is not dependent on sample size

estimation graphics

a graphical representation of an interval estimation in which the focus on the graph is on an effect size, rather than on a null hypothesis

estimation methods

an approach to scientific inference that focuses on estimating the size of an effect rather than on testing a null hypothesis

F-distribution

a continuous probability distribution of all possible values of the F-statistic, usually used in ANOVA and other F-tests. It is asymmetric and has a minimum value of zero but not a maximum value

factorial ANOVA

a statistical procedure with two or more nominal-level independent variables to understand the effect on an interval- or ratio-level dependent variable

factorial between-groups ANOVA

a factorial analysis of variance in which the effects or two or more independent variables are seen through the comparison of scores of different participants observed under separate treatment conditions

factorial within-groups ANOVA

a factorial analysis of variance in which the effects of two or more independent variables are seen through the comparison of scores of the same participants observed under all the treatment conditions

factorial mixed ANOVA

a factorial analysis of variance in which at least one independent variable is a within-groups factor and at least one independent variable is a between-groups factor

Forest plot

a type of graph that summarizes the findings of a meta-analysis

frequency distribution

a graph that shows the frequency of occurrence (y-axis) of the values of a variable (x-axis)

frequency polygon

a graph with a connected series of points in which individual values or ranges of values of an interval-level or ratio-level variable are each represented by a point plotted at a heigh representative of the frequency of those values in a set of data

Frequentist

the view of probability in which probabilities are interrupted as hypothetical long-run frequencies

histogram

a bar graph but there are no arbitrary spaces between individual or ranges of variables

independent-samples t-test

a null hypothesis significance test that compares the difference between the means of two completely unrelated samples to an expected difference between means of 0 in the population

inferential statistics

statistical techniques used to draw conclusions about a population from a sample taken from that population

interval

a scale of measurement where the values are ordered and evenly spaces along some underlying dimension, but there is no true zero

interval estimate

a parameter estimate that defines a range of values within which the parameter may lie

levels of measurement

nominal, ordinal, interval, ratio

line graph

displays data for interval-level or ratio-level dependent variables as a function of interval- or ratio-level independent variables

margin of error

the absolute value of the distance between the center of a confidence interval and the lower and upper bounds of that interval 

matched group design

a study involving two groups of participants in which each member of one group is matched with a similar person in the other group. They are matched on one or more variables that aren’t the main focus of the study but could nonetheless influence the outcome.

mean (arithmetic mean)

a measure of the average value in a data set calculated by adding all the scores and dividing by the number of scores in the data set

median

midpoint of a data set when organized numerically

meta-analysis

an approach to scientific inference that depends on collecting relevant studies that estimate a particular effect size and them summarizing those estimates with meta-analytic statistics and graphics such as a forest-plot

mixed design

a study that combines features of both a between-groups design and a within-groups design

mode

a measure of the most frequently occurring value in a data set

model

in science, a detailed depiction of a phenomenon of interest, usually in mathematical form and usually specifying the important variables involved and the relationship between them

multimodal

a distribution that includes multiple peaks or modes

multiple regression

a statistical technique that is used to describe, explain, or predict (or all three) the variance of an outcome or dependent variable using a score on one predictor or independent variable

negative correlation

a relationship in which two variables change in opposite directions, with one variable increasing and the other decreasing

negatively skewed

a distribution in which the tail on the left side of the distribution is longer than the tail on the right side of the distribution

nominal

a scale of measurement that has unordered categories, which are mutually exclusive

nonparametric test

a type of hypothesis test that does not make any assumptions (e.g. of normality or homogeneity of variance) about the population of interest

normal distribution

a symmetrical distribution with both upper and lower asymptotes, and its mean, median, and mode are the same value

null hypothesis (H0)

the hypothesis that there is no difference between a certain population parameter and another value

null hypothesis significance test (NHST)

a set of procedures used to determine whether the differences between two groups or models are statistically significant

one-sample t-test

a null hypothesis significance test used to compare a sample mean to a population mean

one way/factor ANOVA

an analysis of variance that evaluates the influence of different levels or conditions of a single independent variable upon a dependent variable

one-way between-groups ANOVA

an analysis of variance in which individuals are assigned to only one of several treatments or experimental conditions and each person provides only one score for data analysis

one-way within-groups ANOVA

an analysis of variance in which the events of treatments are seen through the comparison of scores of all the same participants observed under all the treatment conditions

operationalize

precisely defining a variable with specific measurable terms

ordinal

a scale of measurement where the values are ordered along some underlying dimension, but not spaced equally among that dimension

outlier

an observation judged to be so extreme that it may differ in some way from other observations in the sample

p-value

the probability of observing a test statistic or one more extreme when the null hypothesis is true

paired-sample t-test

a null hypothesis test used to compare the mean difference between two related samples; the sample mean difference is compared to an expected mean difference of 0 in the population

parametric test

a hypothesis test that involves one or more assumptions about the underlying arrangement of values in the population from which the sample is drawn

Pearson correlation coefficient

a correlational statistic used to measure linear relationships between variables that have interval-level or ratio-level measurements

point estimate

a parametric estimate that is restricted to a single value of the variable of interest

positive correlation

a relationship in which two variables change in the same direction

positively skewed

a distribution in which the tail on the right is longer than the tail on the left

posterior probabilities

In Bayesian inference, the probability distribution that describes the pattern of beliefs in possible hypotheses after new evidence has been taken into account

prior probabilities 

In Bayesian inference, the probability distribution that describes the pattern of beliefs in possible hypotheses before new evidence has been taken into account 

probability

a value between 0 and 1, inclusive, that represents the long-run relative frequency that a process will yield a particular event

probability distribution

a representation of a set of probabilities

range

the number of values between the minimum and maximum values (max - min)

regression analysis

any of several statistical techniques that are used to describe, explain, or predict (or all three) variance of an outcome or dependent variable using scores on one or more predictor or independent variables

sampling error

the difference between a sample statistic’s estimate of a population parameter and the actual value of the parameter

scatterplot

displays the individual data points in a sample for two interval-level or ratio-level variables

standard deviation

a measure of the typical deviation from the mean (square root of variance)

statistical power

the ability to detect a difference, or relationship, between groups if a difference exists

statistically significant

a result when it is improbable that the null hypothesis is true

t-distribution

a theoretical probability distribution that plays a central role in testing hypothesis about population means, among other parameters

t-test

a statistical test that is used to test hypotheses about two means

two way-factor ANOVA

an analysis of variance design that isolates the main effects of two independent variables, a and b, and their interaction effect, a x b, on a dependent variable

Type 1 error

a statistical error in which the hypothesis test decision was to reject the null hypothesis, when it is actually true; this considered a false positive, the probability of which is represented by a (alpha)

Type II error

a statistical error in which the hypothesis test decision was to fail to reject the null hypothesis, but the null is actually false; considered a false negative, the probability of which is represented by B (beta)

variability

the amount of variation in a group or population

variance 

a measure of the average squared deviations from the mean

within-groups design

an experimental design in which the effects of treatments are seen through the comparison of scores from the same participant observed under all the treatment conditions

zero correlation 

changes in the values of one variable are not related to changes in the value of the other variable