STSCI 2150 Prelim 1

parameter

quantity describing a population

estimate

related quantity calculated from a sample

sampling error

the chance difference between an estimate and the population parameter being estimated

bias

systematic discrepancy between estimates and the population characteristic

random sample

each member of a population has an equal and independent chance of being selected; minimizes bias and makes it possible to measure to amount of sampling error

sample of convenience

a collection of individuals that are easily available to the researcher; may violate assumption of independence

volunteer bias

bias resulting from a systematic difference between the pool of volunteers and the population to which they belong

categorical data

named characteristics of individuals that do not have magnitude on a numerical scale

nominal variable

no inherent order

ordinal variable

can be ordered

numerical data

quantitative measurements that have magnitude on a numerical scale

continuous variable

can take on any real number value within some range

discrete variable

comes in indivisible units

frequency distribution

describes the number of times each value of a variable occurs in a sample

relative frequency distribution

describes the fraction of occurrences of each value of a variable

skew

asymmetry in the shape of a frequency distribution for a numerical variable

percentile

measurement specifies the percentage of observations less than or equal to it; the remaining observations exceed it

cumulative relative frequency

the fraction of observations less than or equal to that measurement

contigency table

gives frequency of occurrences of all combinations of two (or more) categorical variables

principles of graphical display

show the data; represent magnitudes accurately; draw graphical elements clearly, minimizing clutter; make displays easy to interpret; clearly identify the axes

categorical data graph

bar graph

numerical data graph

histogram, cumulative frequency distribution

two categorical variable graph

grouped bar graph, mosaic plot

one numerical and one categorical variable graph

grouped histograms, cumulative frequency distributions, line plot (ordinal only)

two numerical variables graph

scatter plot, line plot, map

coefficient of variation

standard deviation expressed as a percentage of the mean

sampling distribution

the probability distribution of values for an estimate that we might obtain when we sample a population

standard error

standard deviation of the estimate's sampling distribution

standard error of the mean

sample standard deviation divided by the square root of the sample size

confidence interval

range of values surrounding the sample estimate that is likely to contain the population parameter

95% confidence interval

provides a most plausible range for a parameter, values lying within the interval are most plausible, whereas those outside are less plausible, based on the data

2SE rule of thumb

a rough approximation to the 95% confidence interval for a mean can be found from the sample mean plus and minus two standard errors

pseudoreplication

whenever individual measurements are not independent but are analyzed as if they are independent of one another

probability

proportion of times the event would occur if we repeated a random trial over and over again under the same conditions

probability distribution

list of the probabilities of all mutually exclusive outcomes of a random trial

general addition rule

Pr[A or B]= Pr[A] + Pr[B] - Pr[A and B]

Pr[not A]= 1-Pr[A]

general multiplication rule

Pr[A and B]= Pr[A]Pr[B|A]

conditional probability

probability of that event occurring given that a condition is met

Baye's Theorem

Pr[A|B]= {Pr[B|A]Pr[A]}/Pr[B]

law of total probability

the probability of an event X is Pr[X]= all values of Y{Pr[Y]Pr[X|Y]

hypothesis testing

compares data to the expectations of a specific null hypothesis; if the data are too unusual assuming that the null hypothesis is true, then the null hypothesis is rejected

null hypothesis

a specific statement about a population parameter made for the purposes of argument

alternative hypothesis

includes all other possible values for the population parameter

two-tailed test

alternative hypothesis includes values on both sides of the value specified by the null hypothesis

test statistic

quantity calculated from the data that is used to evaluate how compatible the data are with the result expected under the null hypothesis

null distribution

sampling distribution of outcomes for a test statistic under the assumption that the null hypothesis is true

p-value

the probability of obtaining the data (or data showing as great or greater difference from the null hypothesis) if the null hypothesis were true

significance level

alpha, probability used as a criterion for rejected the null hypothesis

Type I error

rejected a true null hypothesis

Type II error

failed to reject a false null hypothesis

power

probability that a random sample will lead to rejection of a false null hypothesis

one-sided test

alternative hypothesis includes parameter values on only one side of the value specified by the null hypothesis