Statistics - Unit 1

population

entire group of people, places, things of interest

parameters

numeric values from the population

sample

small group from population

statistics

numeric values from the sample

measurement bias

values larger or smaller than the true value that are typically caused by incorrectly calibrated instruments

sampling bias

the sample is not representative of the population

voluntary sampling

people with strong feelings one way or the other are the ones tending to respond

convenience sampling

only a "convenient" group is surveyed; this may leave out many subgroups of the population

survivorship bias

focusing on those who made it past some process and not considering those who did not

simple random sampling

a sampling method where all possible participants are equally likely to be chosen

sampling frame

all members of the population are identified and given a numerical label

strata

subgroups of interest

stratified sampling

divide the population into subgroups (strata) and take an SRS from each strata

cluster sampling

all members from a few randomly chosen clusters are selected and interviewed

systematic sampling

every kth subject is sampled

quantitative variables

numerical measurements that record “quantity” (measures or counts)

categorical variables

label outcomes into one of several exclusive groups or categories (qualitative)

frequency

how often each value is observed

data distribution

the way in which data values are spread or arranged across a range of possible values

mode

category with the highest frequency

bar chart

a graphical representation of data using rectangular bars to show the frequency of categories (categorical variables)

histograms

are similar to bar charts but display the frequency distribution of numerical data using adjacent bars of the same width (quantitative variables)

dot plots

similar to histograms but show the original data stacked as dots

shape

the overall layout of the data

center

the centrality or location of the data; where the histogram would be “balanced”

spread

the variation of the data from the minimum to maximum value; describes if data is concentrated in one area or is spread evenly throughout

outliers

any data points that are extremely large or small compared to the majority of the data

diversity

the range and distribution of various traits within a population (categorical)

mean

the average of a data set; the “balancing point”

median

the middle value/observation/data point of an ordered set of data (smallest to largest value)

resistant

a numerical summary that is influenced little by extreme observations (outliers)

measures of spread

variation/variability in the data

range

the largest observation minus the smallest observation

standard deviation

a measurement of the typical/average distance of observations from the mean

interquartile range (IQR)

measures the range of the middle 50 percent of data

percentiles

the pth percentile is the measurement to which p percent of all measurements fall below it and (100-p) percent lie above it

quartiles

special percentiles that divide the data into quarters

how to find IQR

IQR = Q3 - Q1

how to find the step

1.5 (IQR)

how to find the upper fence

Q3 + step

how to find the lower fence

Q1 - step

side by side bar graphs

bar graphs that compare two categorical variables

side by side box plots

separate box plots are constructed on the same axis for each level of a categorical variable

side by side dot plots

separate dot plots constructed for each level of a categorical variable

scatterplots

easy way to study the relationship between two quantitative variables measured on the same subject or at the same point (plotted (x,y))

explanatory variable

one variable that exerts influence on the other (x axis)

response variable

what is impacted or what responds to the explanatory variable