statistics definitions

effect size

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power

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sampling distribution of M

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statistical assumption

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x-scores

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histogram

a bar graph that shows the frequency of data within equal intervals

discrete variable

a quantitative variable whose values are countable

nominal-level variable

categorical-discrete

symmetrical distribution

A distribution that, when bisected by a vertical line, is identical on both sides.

test statistic

A number that summarizes the data for a test of significance; usually used to obtain P-value.

statistic

A numerical measurement describing some characteristic of a sample

frequency table

A table that lists items together according to the number of times, or frequency, that the items occur

continuous variable

A variable (such as age, test score, or height) that can take on a wide or infinite number of values.

skewed distribution

An asymmetrical distribution of scores on some variable, with scores clustering toward the high or low end of the possible range of values.

Type II error

Error of failing to reject a null hypothesis when in fact it is false (also called a "false negative"). You think there is NO CAUSE EFFECT but THERE IS

type I error

Error of rejecting null hypothesis when in fact it is true (also called a "false positive"). You think you found a cause effect relationship but ONE IS NOT THERE

parametric statistics

Involve numbers with known, continuous distributions; when the data are interval- or ratio-scaled and the sample size is large, parametric statistical procedures are appropriate.

research hypothesis

States that a relationship or direction exists between variables. Is scientific, substantive, theoretical, & declarative.

observed statistic

The value of the statistic computed from the data..

negative skewed

data, the distribution's tail extends to the left, in a negative direction

variability

in a set of numbers, how widely dispersed the values are from each other and from the mean

Empirical research study

making decisions about the world based on observations and measurements of reality. experimental study

z-scores

measures distance (in units of standard deviations) from the mean

measures of variability

measures that indicate the degree of dispersion or spread of the data; include range, variance, and standard deviation

measures of central tendency

numbers that are used to describe the center of a set of data. These measures include the mean median and mode

interval-level variable

order, rank, equal distance-continuous

homogeneity of variance

the assumption of analysis of variance is that variances of the observations in the individual groups are equal. Can be tested through an ANOVA to determine how the total variance can be divided into what is error and what was effected by the treatment

mean

the average

directional hypothesis test

(Ho and H₁) make a statement about the direction of the effect; either an increase or a decreas in the population mean

positive skewed

(skewed distribution) contains more low scores than high scores, tail on right

weighted mean

The mean of a set of numbers that have been weighted (multiplied by their relative importance or × of occurrence).

standard normal distribution

The normal distribution with mean µ = 0 and standard deviation σ = 1. Its ordinary scores are the same as its z-scores.

degrees of freedom

The number of individual scores that can vary without changing the sample mean. Statistically written as 'N-1' where N represents the number of subjects.

distribution of means

the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population

critical region

the most extreme portion of a distribution of statistical values for the null hypothesis determined by the alpha level (typically 5%)

mode

the most repeated number

standard deviation

the square root of the variance, a measure of variability that describes an average distance of every score from the mean

sample

the subset of the target population of objects or participants that is selected for research investigation. A sample is the part of a population that is observed. A sample must be selected in such a way as to avoid presenting a biased view of the population, A biased estimate is one that is for some reason overestimates or underestimates what is being measured.

critical statistic

the value of the statistic that bounds the critical region.

ratio-level variable

true zero point-continuous

ordinal-level variable

categorical, ordered/ranked-discrete

cutoff score

point in hypothesis testing, on the comparison distribution at which, if reached or exceeded by the sample score, you reject the null hypothesis.

raw scores

scores that have not been averaged, sorted, or processed yet

standard scores

scores that represent an individual's relative deviation from the mean of the standardization sample

Inferential statistics

statistical procedures designed to establish the probability of a causal relationship existing between sets of empirical observations. These can be correlational statistics or tests for difference/variance

descriptive statistics

statistical procedures designed to present research data in summary form, including central tendency, dispersion, and graphical displays.

non-parametric statistics

the branch of statistics dealing with variables without making assumptions about the form or the parameters of their distribution

median

the middle number

dependent variable

the variable in which the values may depend on changes in an independent variable.

Independent variable

the variables whose categories are manipulated in an experiment.

transformed scores

this represents any score that has been changed from a raw score in a systematic way - this is done so that test results can be more easily compared

sampling error

The amount of error associated with a sample due to its deviation from the population

standard error

The estimated standard deviation of the error in that method of estimation or estimation. It therefore estimates the standard deviation of the sample mean based on the population. Specifically, it estimates the standard deviation of the difference between the measured or estimated values and the true values. Note that while this definition makes no reference to a normal distribution, many uses of this quantity implicitly assume such a distribution.

null hypothesis

The hypothesis that states there is no difference between two or more sets of data.

theory

a body of knowledge and interpretation in a particular area, supported by testable observation, plus a particular interpretation. A theoretical discipline is concerned with developing, exploring or testing the theories or ideas that researchers have about how the world operates.

two-tailed test

a hypothesis that does not specify a direction. For example, if your hypothesis is that your program or intervention will have an effect on an outcome, but you are unwilling to specify whether that effect will be positive or negative, you are using a two-tailed hypothesis.

one-tailed test

a hypothesis that specifies a direction; for example, when your hypothesis predicts that your program will increase the outcome.

variance

a measure of the statistical dispersion of a data set or distribution, indicating how its possible values are spread around the mean.

parameter

a quantity (such as the mean or variance) that characterizes a statistical population and that can be estimated by calculations from sample data

Variables

a set of scores that can vary

operational definition

a statement of the procedures (operations) used to define research variables. For example, human intelligence may be operationally defined as what an intelligence test measures

normal distribution

a symmetrical, bell-shaped curve that describes the distribution of many types of data; most scores fall near the mean (68% fall within one standard deviation of it) and fewer near the extremes

non-directional hypothesis test

a two-tailed test, critical region of 1.96. Need large deviations for population mean

bar graph

a type of graph in which the lengths of bars are used to represent and compare data in categories

population

all the members of a uniquely definable group of people or things. A statistical population is a set of entities about which statistical inferences are to be drawn, often based on a random sample taken from the population. The term 'population' is also used to refer to a set of measurements or values.

construct

an abstract or general idea inferred or derived from specific instances