Purdue STAT 301 Exam 1

Categorical variable

a variable that is described in WORDS (ex: eye color)

Quantitative variable

a variable that is described in NUMBERS (ex: weight)

Bar graphs are used for

categorical data

Pie charts are used for

quantitative data

Stemplots

are tables in which NUMERICAL (quantitative) data values are divided into "stems" that can have multiple "leaves"

Histograms

are graphs consisting of vertical bars that touch each other and represent the frequency distribution of a set of data (quantitative)

bar graph

pie chart

Stemplot

Histogram

Outliers

extreme values that don't appear to belong with the rest of the data

influential observation

an observation that has a strong influence or effect on the regression results

1 peak=

unimodal

2 peaks=

bimodal

more than 2 peaks=

multimodal

symmetric

mean is equal to median

right skewed

mean is greater than median

left skewed

mean is less than median

Center of Distribution

Described by the mean, median, or mode, it is in some way the middle of the distribution.

Spread of Distribution

Described by Range, Interquartile Range, or Standard Deviation, the spread says how "wide" the distribution is.

Outliers

Any point that falls outside the pattern of the association should be considered an outlier.

Influential Points

A point is influential if it has a big effect on a calculation, such as the correlation or equation of the least-squares regression line. Points separated in the x-direction are often influential.

Mean

only used when data is NOT skewed, only used with continuous data (ratio or interval)

Median

used when data IS SKEWED, aka 50% percentile, normal distribution curve, can be used with all the data types

range

the difference between the highest and lowest scores in a distribution

IQR (interquartile range)

measure of statistical dispersion, being equal to the difference between the upper and lower quartiles (IQR = Q3 − Q1)

Variance

a difference between what is expected and what actually occurs (standard deviation squared)

standard deviation

a computed measure of how much scores vary around the mean score (square root of variance)

resistant measure

A statistic that is not affected very much by extreme observations.

5 number summary

minimum, Q1, median, Q3, maximum

1.5 IQR Rule

used for identifying outliers, any values that are more than 1.5 times the IQR lower than the first quartile or higher than the third quartile are called outliers

Boxplots (modified)

Boxplots (side-by-side)

unit/subject

one member of the entities being studied

Population vs. Sample

The population is the whole group versus a sample which are parts of the population.

Census

the official count of a population

Experiment

A study is an experiment ONLY if researchers impose a treatment upon the experimental units.

Observational Study

In an observational study, researchers make no attempt to influence the results and cannot conclude cause-and-effect.

non-random sampling

an alternative sampling method to random sampling, where the sample is not chosen at random.

voluntary response sample

A sample which involves only those who want to participate in the sampling

simple random sample (SRS)

every member of the population has a known and equal chance of selection

stratified random sampling

separation of the target population into different groups, called strata, and the selection of samples from each stratum

Multistage Random Sampling

a sample design in which the elements of the sampling frame are subdivided and the sample is chosen in more than one stage

anecdotal evidence

an informal observation that has not been systematically tested

undercoverage bias

occurs when some groups in the population are left out of the process of choosing the sample

nonresponse bias

bias introduced to a sample when a large fraction of those sampled fails to respond

response bias

people do not respond honestly

sampling variability

the natural tendency of randomly drawn samples to differ from each other

Parameter vs. Statistic

a characteristic or measure of a POPULATION vs. a characteristic or measure of SAMPLE

sampling distribution

the distribution of values taken by the statistic in all possible samples of the same size from the same population

treatments

the experimental conditions imposed by the experimenter

Factors

used during an experiment in order to determine their effect on the response variable

Factor levels

factors can only assume a limited number of possible values

explanatory variable

a variable that we think explains or causes changes in the response variable

response variable

a variable that measures an outcome or result of a study

control group

the group that does not receive the experimental treatment

Placebo

something which has a positive mental effect, but no physical effect

Bias

something that causes an inaccuracy in statistics and should be avoided

3 principals of experimental design

control, randomization, replication

completely randomized design

the treatments are assigned to all the experimental units completely by chance

block design

the random assignment of individuals to treatments is carried out separately within each block (group A and group B)

matched pairs design

A method of assigning subjects to groups in which pairs of subjects are first matched on some characteristic and then individually assigned randomly to groups.

double-blind experiment

an experiment in which neither the experimenter nor the participants know which participants received which treatment

review board

screening committees at research institutions that evaluate all research projects relative to their potential harm to participants

informed consent

an ethical principle that research participants be told enough to enable them to choose whether they wish to participate

Confidentiality

the act of holding information in confidence, not to be released to unauthorized individuals

ethics of doing experiments with animals

reduce, refine, replace

Causation

A cause and effect relationship in which one variable controls the changes in another variable.

lurking variable

a variable that is not among the explanatory or response variables in a study but that may influence the response variable

68-95-99.7 rule

in a normal model, about 68% of values fall within 1 standard deviation of the mean, about 95% fall within 2 standard deviations of the mean, and about 99.7% fall within 3 standard deviations of the mean

standard normal distribution

a normal distribution of z scores

sample mean symbol

x̅

standard deviation symbol

weird looking "o" that is actually a Greek letter that I do not know the name of (sorry)(maybe sigma?)

population mean symbol

μ

Central Limit Theorem (CLT)

the sampling distribution derived from a simple random sample will be approximately normally distributed