Statistics vocab

Statistical Thinking

Involves critical thinking and the ability to make sense of results, demanding more than just the ability to execute complicated calculations.

Data

Collections of observations, such as measurements, genders, or survey responses.

Statistics

The science of planning studies and experiments; obtaining data; and organizing, summarizing, presenting, analyzing, and interpreting those data and then drawing conclusions based on them.

Population

The complete collection of all measurements or data that are being considered and which one would like to make inferences about.

Census

The collection of data from every member of a population.

Sample

A subcollection of members selected from a population.

Prepare

The first phase of a statistical study consisting of considering the Context, the Source of the Data, and the Sampling Method.

Analyze

The second phase of a statistical study consisting of Graphing the Data, Exploring the Data (looking for outliers and missing data), and Applying Statistical Methods.

Conclude

The final phase of a statistical study where one determines if the results have Statistical Significance and Practical Significance.

Voluntary Response Sample

Also known as a self-selected sample, it is one in which the respondents themselves decide whether to be included.

Statistical Significance

Achieved in a study if the likelihood of an event occurring by chance is $5\%$ or less.

Practical Significance

A finding that is effective but does not make enough of a difference to justify its use or be considered useful in a common-sense context.

Nonresponse

A potential pitfall in data analysis that occurs when someone either refuses to respond or is unavailable.

Loaded Questions

Survey results that are not worded carefully and can result in misleading information.

Low Response Rates

A situation where a low number of participants respond, decreasing the reliability of results and increasing the likelihood of bias.

Parameter

A numerical measurement describing some characteristic of a population

Statistic

A numerical measurement describing some characteristic of a sample

Quantitative data

consists of numbers representing counts or measurements

Categorical data

consists of names or labels (not numbers that represent counts/measurments)

Discrete Data

results when the data values are quantitative and the number of values is finite or countable

Continious data

result from infinitely many possible quantitative values where the collection of values is not countable

Levels of measurement

Nominal- categories only

ordinal- categories with some order

interval- differences but no natural zero point

ratio- differences and a natural zero point

Experiment

Apply some treatment and then observe its effects on the individuals (called experiemental units)

Observational study

Observe and measure specific characteristics without attempting to modify the individual being studied

replication

the repetition of an experiment on more than one individual

blinding

A technique where the subject doesnt know whether they are receiving a treatment or a placebo

Double-blind

when neither the subject or the experiementer knows if they have a placebo or not

Randomization

when subjects are assigned to different groups through random selection

Simple random sample

A sample of n subjects is selected in a way that every possinle sample of the same size n has the chance of being chosen

Systemic sampling

select some starting point and then every kth element in the population

Convenience sampling

data that is easy to get

Stratified sampling

subdivide the population into at least two different subgroups so that the subjects within the same subgroup share the same characteristics

cluster sampling

divide the population area into sections then randomly select some clusters and choose all the members from selected clusters

multistage sampling

collect data by using a combination of the basic sampling method

observational studies

observe and measure but do not modify

Cross-sectional study

data collected at one point in time

retrospective (case control) study

Data collected from the past

prospective (longitudinal or cohort) study

Data collected in the future from groups sharing common factors

Confounding

occurs when we see some effect but we cant identify the specific factors that caused it

Distribution (or frequency table)

shows how data are partioned among several categories by listing the categories along with the number of data values in each of them

Lower class limit

the smallest numbers that can belong to each of the different classes

upper class limit

the largest numbers that can belong to each of the different classes

class boundaries

the numbers used to separate the classes, but without the gaps created by class limits

class midpoints

the values in the middle of the classes, each midpoint can be found by adding the lower class limit to the upper class limit and dividing by two

class width

the difference between two consecutive lower class limits

procedure for constructing a frequency distribution

Class width = (maximum data value) - (minimum data value)

. number of classes

relative frequency for a class

= frequency for a class /

sum of all frequencies

percentage for a class

= frequency for a class/

sum of all frequencies x 100

comparisons

combining two or more relative frequency distributions in one table makes comparing data easier

in statistics, we are interested in finding whether or not the data has a

normal distribution

Presence of gaps on a chart

can show that the data are from two or more different populations

histograms

a graph consisting of bars of equal width drawn adjacent to each other

analyzing a histogram can be done using

CVDOT

CVDOT

The CENTER of the data

the VARIATION

the width of the DISTRIBUTION

whether there are any OUTLIERS

TIME

Skewness

a distribution of data is skewed if it is not symmetric and extends more to one side than the other

normal distribution

the pattern of the points in the normal quantile plot is reasonably close to a straight line and the points do not show a systemic pattern that isnt a straight line

not a normal distribution

the population distribution is not normal if the normal quantile plot has either or both

Measure of center

a value at the center or middle of a data set

Mean

the measure of center found by adding all of the data values

median

the measure of center that is the middle value when the original values are arranged in order of increasing/decreasing order

mode

the value that occurs with the greatest frequency

midrange

the measure of center that is the midway value between the maximum and minimum values in the original data set

range

the difference between the maximum and minimum data value

s

sample

σ

population

s²

sample variance

σ²

population variation

z-score

the number of standard deviations that a given value is above or below the mean