Unit 8 Univariate Statistics

center

the typical value of the distribution, described my measures of center

shape

describes the overall pattern of the distribution

uniform

even frequencies in a model, all bars are similar

mean

arithmetic average (add all values, divide by number of values)

IQR

interquartile range, measures spread of the middle 50% of data

distribution

how much data values are spread out, clustered, or frequency distributed

box plot

a model that summarizes data using the minimum, Q1, the median (Q2), Q3, and the maximum

Standard deviation

the square root of the variance used to describe average amount of variation in a data set

Confidence interval

an interval/range of values a statistician hopes will contain the true parameter based on statistical calculations involving the empirical rule

Standard error

measures how much sample statistics vary from sample to sample (root (p

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95

Randomness

when we know what outcomes are possible but not which particular thing will occur

Parameter

a fixed, numerical value that describes an entire population’s characteristics (mean, standard deviation)

Mean absolute deviation

the average absolute distance from the mean (|actual

Voluntary response bias

individuals must volunteer or take some prior action to be included in a sample

Nonresponse bias

a substantial amount of samples fail to respond

stratified sample

first, divide population into groups (strata) based on similarities. Then, choose a random sample from each group

Observational study

study where the researchers do not assign treatments, they simply observe them

Treatment

a specific condition applied to experimental units to measure its effect on a variable

Comparison

we must compare the results between 2 or more treatments/groups

Control

keeping other variables constant between different treatment groups

Blinding

either subjects or evaluators don’t know which treatment the subjects are getting

outlier(s)

a data point that lies an extreme distance from the other data values

Spread

how variable or dispersed data is, explained through measures of spread

Skew (left/right)

tail of the data in the model is left or right

Symmetrical

balanced and even data on both sides

Unimodal

1 peak of data

Bimodal

2 peaks of data

Median

middle value when data is arranged least to greatest, is the midpoint of data and separates the lower and upper halves

Mode

the value that appears most often, is the most common value

Range

the total spread of data from the highest to lowest value

maximum/minimum

the highest/lowest value in a data set

Stem plot

organizes data by place value

Dot plot

displays individual data values using dots and a number line

Histogram

groups data into intervals called bins, represents frequency within intervals

Percentile

The value below which a given percentage of observations in an ordered data set falls

Quartile (1st and 3rd)

25% or 75% of the data in the data set lies below

Central limit theorem

if a large enough sample is taken, then the sampling distribution of the mean/statistic for that random variable will be about a Normal distribution

Sampling distribution

the distribution of a statistic calculated from MANY repeated random samples of the same size from a population

Normal distribution/curve

a unimodal, symmetric curve

Margin of error

tells how far the sample statistic may reasonably be from the true population parameters

Simulation

generation random data from a known probability distribution to understand the behavior of a single variable

Variability

measures how spread out of dispersed data points are, indicating how much they differ from each other and from the center

Sample

a piece of data collected from a larger population to analyze a single variable

Population

An entire set of individuals that share a common characteristic

Mean deviation

the average distance of data values from the center ((actual

Statistics

a numerical value calculated from a single variable to summarize its distribution, central tendency, or dispersion

Bias

any collecting of data in which some characteristic of the population is overemphasized or underemphasized

Variance

measures the average squared distance from the mean ((actual

Undercoverage bias

some portion of the population is not sampled at all or has a reduced chance of being included in the sample

Convenience sampling bias

sample chosen due to how easy it is

Simple random sampling

each member of the population has an equal chance of being sampled

Response bias

anything in a survey design that influences the responses

systematic sampling

list the whole population and randomly select a member from the first n numbers. Then, select every nth number after

Cluster sampling

first, divide the population into heterogeneous groups. Then, randomly choose which groups to sample

Response variable

the variable whose resulting values are compared across different treatments

Experiment

researchers assign treatments to determine causation between 2 variables

Subjects

humans on whom the experiment is performed

Experimental units

the objects on whom the experiment is performed

Replication

using a large enough amount of subjects/objects

Randomization

must assign subjects to treatments randomly

Placebo effect

a perceived reaction to an ineffective treatment

Placebo

a treatment known to have no effect, administered to the control group

Double blinding

both the subjects and evaluators don’t know who is part of which treatment groups