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