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Standard Deviation

An estimate of the average variability (spread) of a set of data

Standard Error of the Mean

The standard deviation of the sampling distribution of a statistic (the mean)

Standard Error of Measurement

Standard deviation of a persons' repeated test scores; inversely related to reliability (ex. reliability = 1.0, SEM = 0); helps you figure out what will probably happen if the subject takes the same test again

population proportion

pi (π)

population mean

mu (µ)

population standard deviation

lower case sigma (σ)

sample proportion

p-hat (p̂)

sample mean

x-bar (x̄)

s

sample standard deviation

Observational Study

Attempts to collect information and draw conclusions about a population of interest without influencing the results.

Experiment

Attempts to find cause-effect relationships by imposing some kind of treatment on the experimental units.

Bias

The study systematically favors a certain conclusion.

Sampling Bias

Bias that is connected to the sampling process. For example: If the selection comes from people who have phones, those without phones may tend to respond differently. They are under represented.

Non-Sampling Bias

Bias related to the process of gathering information from the selected sample.

Natural Variation

Inherent deviation between the sample result and the population.

Anecdotal

The use of personal experience or one counter example to a widely accepted conclusion in order to debunk.

Median

The point of equal area

Mean

The point where if the figure were made of solid material the weight would be even.

Percentile

The proportion of data or the curve that is below a given value.

Confidence Intervals

Attempt to capture a value that describes the population based on a sample value called a statistic.

n

sample size

μ

Mu, population mean

σ

population standard deviation (lower case sigma)

S^2

sample variance

σ^2

population variance

p^

sample proportion

p

population proportion

mode

value that appears the most

Range

is the highest score minus the lowest score (some exams will add 1 to the answer). e.g., 24, 46, 3, 26, 47. 47 - 24 = 23 + 1 = 24

variance

(Σ(x-xbar)^2)/(n-1)

correlation

the extent to which variables are related

High Standard Deviation

The data are widely spread

Error Bars

Graphical representation of the variability of data

68%

±1 of Standard Deviation

95%

±2 of Standard Deviation

t-Test

A test used to find out whether there is a significant difference between the means of two populations

Q1

median of the lower 50 percent of ranked data

Q3

median of the upper 50 percent of ranked data

IQR

measure of variability that represents the range of the middle half of the data

ΣX^2

The symbol for the sum of the squared Xs

(ΣX)^2

The symbol for the squared sum of X

S^2X

The symbol for sample variance

SX

The symbol of sample standard deviation

σ^2x

The symbol used when describing the true population variability

s2X

The symbol used to estimate the variability in the population

biased estimator

A formula for a sample's variability that invalid dividing by N is biased toward underestimating the corresponding population variability

degrees of freedom

The number of scores in a sample that are free to vary, and thus the number that is used to calculate an estimate of the population variability; symbolized by df

estimated population standard deviation

The unbiased estimate of the population standard deviation calculated from sample data using degrees of freedom (N-1)

measure of variability

Measures that summarize the extent to which scores in a distribution differ from one another

population variance

The average squared deviation of scores around the population mean

proportion of variance accounted for

The proportion of the error in predicting scores that is eliminated when, instead of using the mean of Y, we use the relationship with the X variable to predict Y scores; the proportional improvemen…

sample standard deviation

The square root of the sample variance or the square root of the average squared deviation of sample scores around the sample mean

sample variance

The average squared deviation of a sample of scores around the sample mean

sum of the squared Xs

A result calculated by squaring each score in a sample and adding the squared scores

unbiased estimator

A formula for a sample's variability that involves dividing by N-1 that equally often under- and over-estimate the corresponding population variability