GLBL 2121 Vocabulary

descriptive statistics

the process of describing/summarizing sample/population data collected

inferential statistics

the process of making predictions about population parameters using the data

population

the entire group of interest in regards to a statistical study

sample

a section of the entire group of interest of study

variables

characteristics that vary among subjects

quantitative

numerical values that represent different magnitudes of the variable

qualitative

values that are categorical without a specific order or magnitude

nominal data

measurements that are categorical/qualitative and unordered (no category is greater than or smaller than any other)

ordinal data

measurements that are categorical/qualitative and ordered (however, there is no particular defined distance between the levels of data)

discrete variables

values that form a set of separate numbers

continuous variables

values that can form an infinite continuum of possible real number values

n

sample size

simple random sample

method for creating a sample population in which each possible sample within that population has the same probability of being selected

sampling frame

list of all subjects in a population

random numbers

numbers generated by a computer to facilitate the selection of random samples in SRS

sample survey

method of collecting data involving supplying samples with questions

experiment

data gathered from the process of systematically changing a/certain condition(s) and measuring the output

treatments

different conditions within an experiment

observational studies

study of a population/sample without any manipulation of conditions

sampling error

how much the statistic differs from the parameter it predicts because samples are variable from the larger population

sampling bias

a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability and may thus have adverse effects on the data collected

nonprobability sampling

methods for which it is not possible to determine the probabilities of the possible samples (i.e. volunteer sampling)

selection bias

bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population intended to be analyzed

undercoverage

when the sample selected for a study lacks representation from some groups in the population

response bias

wide range of tendencies for participants to respond inaccurately or falsely to questions

nonresponse bias

inability to gather data from certain subjects within a sample, either because of their refusal to participate or they are unreachable

systematic random sampling

process of selecting subjects by choosing a subject at random from the first nth name within a sampling frame and then selecting every nth subject listed after that one.

stratified random sampling

process of selecting subjects by dividing the population into separate groups called strata and then selecting a simple random sample from each stratum

proportional stratified random sampling

occurs when the sampled strate proprtions are the same as those in the entire population

disproportional stratified random sampling

occurs when the sampled strate proportions differ from the population proportions

cluster sampling

process for selecting subjects in which the population is divided into large number of clusters and a simple random sample is selected from amongst the clusters

multistage sampling

process for selecting samples by which mulitple sampling methods are utilized

frequency distribution

list of possible values for a variable with # of observations for that variable

relative frequency distribution

frequency distribution but with percentages/proportions

histogram

frequency distribution for quantitative variables segmented by intervals

stem-and-leaf plots

observations presented with their leading digit (stem) and final digit (leaf)

population distribution

frequency distributions for populations

sample data distribution

frequency distribution for samples

symmetrical distribution types

U-shaped and bell-shaped

skewed distributions

when the extreme ends of data frequencies form “tails” that elongate the shape

mean (average)

sum of the observations divided by the # of observations

y-bar

sample mean

properties of the mean

(1) highly influenced by outliers

(2) influenced by skewed distributions

(3) the “point of balance” on a number line when an equal weight is at each observation point

weighted average

where two sets of data with sample sizes n1 and n2 with sample means y1 and y2 are combined: (n1y1 + n2y2) / (n1 + n2)

median

the observation that falls in the middle of the ordered sample

properties of the median

(1) valid for quantitative and ordinal data

(2) for symmetric distributions, median and mean are the same

(3) in skewed distributions, it lies less farther out along the tail than the mean

(4) insensitive to the distances of the observations from the middle (only uses order of the data)

(5) not affected by outliers

best case use for mean

highly discrete data; distribution is close to symmetric or only mildly skewed

best case use for median

highly skewed data

mode

the values that occurs most frequently

bimodal distribution

when two distinct clusters of data occur within a data distribution

range

the difference between the largest and smallest observations within a data set

standard deviation

a measure of the amount of variation of the values of a variable about its mean; found by computing the squared sum of squared deviations from the y-bar mean and dividing by the sample size n—1; denoted by s

variance

standard deviation squared; denoted by s-squared

sum of squares

the sum of all calculated deviations squared; the larger the deviations, the larger the sum of squares and the larger s tends to be

properties of standard deviation

(1) s always greater than or equal to 0

(2) s = 0 when all the observations have the same value

(3) the greater the variability about the mean, the larger is the value of s

(4) standard deviation can be “rescaled” by multiples

percentiles

indicate the percentage of observations that fall below or at that point; the percentage of data falling above it = (100 - p)%

lower quartile

25th percentile

quantile

50th percentile

upper quartile

75th percentile

IQR (interquartile range)

different between the upper and lower quartiles; describes the spread of the middle half of the observations (increases as variability increases); not as sensitive as standard deviation is to outliers; for bell-shaped distributions, the IQR is approximately (4/3)s

boxplot

graph display that captures center (median) and variability (quartiles); extends to minimum and maximum but does not encapsulate outliers

outlier

falls more than 1.5(IQR) above the upper quartile and more than 1.5 IQR below the lower quartile

z-score

the # of standard deviations that an observation falls from the mean

association

exists between two variables if certain values of one variable tend to go with certain values of the other

bivariate analysis

an analysis of association between two variables (usually explanatory and response variables)

explanatory variable

the variable that defines groups (independent variable)

response variable

the outcome variable (dependent variable)

contingency table

displays the # of subjects observed at different combinations of possible outcomes for the two variables; illustrates contingency between explanatory variable and outcome

scatterplot

graph that plots data between bivariate quantitative variables using one dot to represent one occurence of that outcome

correlation

describes the strength of association between variables in terms of how closely the data follows a straight-line trend

regression analysis

analysis method that provides a straight-line formula for predicing the value of y given a value of x

μ

population mean; average of the observations for the entire population

σ

population standard deviation; describes the variability of those observations about the population mean

probability

the proportion of times that the outcome would occur in a very long sequence of observations

probability of A not occurring

P (not A) = 1-P(A)

probability of A or B

P (A or B) = P(A) + P(B)

probability of A and B

P (A and B) = P(A) x P(B given A); contains a conditional probability

probability of A and B (independent)

P(A and B) = P(A) x P(B)

histogram

graphic display for probability distribution where the probability of a value is represented by the height of a bar

mean of a probability distribution (discrete)

sum of total observations times their probability of occurence

E(y)

expected value of y; also known as the mean of a probability distribution

normal probability distribution

symmetric, bell-shaped, and characterized by its mean (μ) and standard deviation (σ); 0.68 of observations fall within 1 standard deviation, 0.95 within 2 SDs, and 0.997 within 3 SDs

Empirical Rule

for bell-shaped histograms, about 68% of the data fall within 1 SD of the mean, 95% falls within 2 SDs of the mean, and 99.7% of data falls within 3 SDs of the mean

z-score

represents the # of SDs that observed value y falls from the mean

standard normal distribution

a normal distribution with the mean μ = 0 and the SD σ = 1

covariance

represents the average of the cross products about the population means between bivariate variable distributions (joint probabilities for pairs of random variables)

sampling distribution of a statistic

the probability distribution that specifies probabilities for the possible values that statistic can take (i.e. sample proportion or sample mean)

sample mean y in relation to population mean μ

fluctuates (sample mean y varies in value from sample to sample)

standard error

the standard deviation of the sampling distribution y; describes how sample mean y varies from sample to sample; denoted by σ(y)

as n increases, the standard error

decreases

as n increases, the sampling distribution gets

narrower (sample proportion falls closer to the population proportion; less probability of getting any other wild answer)

Central Limit Theorem

for random sampling with a large size n, the sampling distribution of the sample mean y is approximately a normal distribution; for most cases, n of 30 is sufficient

implication of Central Limit Theorem

the bell shape of the sampling distribution applies no matter the same of the population distribution