STAT exam 1

What is statistics?

Statistics is about….variation.

General Terms (3)

Population

Sample

Case

Population

group of all cases that the sample was selected from

i. “All ...”

Sample

group of cases that we collect data from

i. “Number of Sample ...”

Case (Unit

who or what we collect data from

i. “A ...”

Variables

Categorical

Quantitative

Explanatory

Response

Categorical:

Each case is assigned to a specific group or category (eye color,

letter grade, etc.)

“What type?”

Quantitative:

Requires measurement and has units, a numerical amount

(weight, height, etc.)

“How much/how many?”

Explanatory:

used to try to explain the variability in the response values.

1. “________ (explanatory variable) is the explanatory variable

because it is predicting __________ (response variable).”

Response:

an outcome variable on which comparisons are made.

1. “__________ (response variable) is the response variable because

it is being predicted.”

Types of Analysis

Descriptive

Inferential

Descriptive:

A technique that summarizes both old and new data to identify trends and patterns.

1. Just a description of what the data says, not drawing conclusions or making decisions based on the data

Inferential:

uses samples of data to make inferences, predictions, andgeneralizations of the entire population.

1. Can make decisions based on data

Types of Studies

Experimental vs. Observational

Experimental:

1. Random assignment is present → it is an experiment

a. Treatment that is randomly assigned

b. Active manipulation

Observational:

1. No random assignment present → it is an observational study

a. Even if there is a treatment being manipulated, no random assignment then it MUST be observational

Differences between Experimental vs. Observational:

i. Presence or lack of randomly assigned treatment

ii. When asked: “Is this study an experiment or an observational study?”

...

1. Experiment: “It is an experiment because the treatment was randomly assigned”

2. Observational Study: “It is an observational study because there was no random assignment of treatment”

Types of Conclusions & How they Relate to Randomness

Random Assignment

1. How treatments are being assigned to people already in the sample

2. Random assignment ensures any confounding variables are balanced in the sample, so the only difference between groups is the manipulated treatment

allows cause and effect of SAMPLE

Random sampling

1. Who is being pulled to be in the sample

2. Random sampling ensures the sample accurately represents the population of choice

allows generalizations of the POPULATION

Observational Studies have… (4)

a. Sample Surveys

b. Sampling Techniques (Positives/Negatives)

c. Bias – What is it?-

d. Retrospective vs. Prospective

Types of Sampling Techniques (Positives/Negatives)

Simple Random Sample (SRS)

Stratified Sample

Cluster Sample

Simple Random Sample (SRS):

Each combination of cases has the same chance of being included

Stratified Sample:

Divide population into strata (where everyone in each strata has some similarity) and select a SRS from each strata

Cluster Sample:

Divide population into clusters with mix of representatives (each cluster should be a mixed group of subjects, no key similarity linking them), select clusters at random

Types of Bias: (3)

Sampling Bias

Non-response Bias

Response Bias

Bias – What is it?-

the systematic error that leads an estimate to differ from the true value of the parameter being measured

Sampling Bias:

occurs when the sample collected is not representative of the population, leading to distorted or inaccurate conclusions.

Non-response Bias:

occurs when individuals selected for a survey or study do not respond, and their non-participation is related to the subject of the study

Response Bias:

bias occurs when participants in a survey or study give inaccurate or false answers, often due to the wording of questions, social pressure, or misunderstanding

Retrospective:

study that looks backward, old/previous data that we can observe and understand

Prospective:

study that looks forward, new/future data that we will collect and make predictions

Experiments (3 parts)

a. Understand process & flow of experiment

b. Terms

c. Designs

Experiment terms: (9)

Factor

Levels

Treatment

Experimental units

Response

Control (2 types)

Randomness & their Purpose (2 types)

Replication (2 types)

Blinding

Factor:

a. Explanatory variable(s), what you manipulate

i. If only 1 factor in experiment → levels and treatment will be the exact same

Levels:

Values used within a factor, at least two for each factor

Treatment:

The combination of factors and levels given to experimental units

i. For 2+ factors, this will be every possible combination of levels between each factor

Experimental units:

What the treatment is being applied to (and what is giving us a response)

Response:

What is being measured after treatment has been applied

i. Quantitative or categorical

Control (2 types):

a. Control group (what we compare against, as a baseline to the treatment group)

b. Control of outside variables (via random assignment, making control and treatment groups identical, besides the treatment)

Randomness & their Purpose (2 types):

Random Assignment (balance out confounding variables)

Random Sample (accurate representation of the population)

Replication (2 types)

a. Multiple replicates (multiple cases) within an experiment/experiment group

b. Repeating the entire experiment

Blinding:

Who has knowledge of the treatment applied

Designs (3)

(see flow charts in the lecture notes for better understanding)

Completely Randomized Design (CRD)

Block Design

Matched Pairs Design

Completely Randomized Design (CRD):

One sample group, random assigned to treatments, compare the responses between the treatment groups

Block Design:

a. Identifiable difference between experimental units used to separate experimental units into different groups

b. Similar to CRD, but subjects are blocked and then each block gets a CRD

Matched Pairs Design:

a. Each experimental unit gets both 2 treatments OR experimental units are paired by similar characteristics, and each gets one of the treatments

Displaying Single Variable Data (3)

Bad vs Good Graphs

Categorical

Quantitative

Bad vs Good Graphs:

Bad Graph:

1. Not labeling axis

2. Inconsistent scale

3. Using 3D images

4. Pie Charts

5. Not starting at zero

Good Graph:

1. Don’t do the above

Categorical Graph:

Pie Chart, Bar Graph

1. DO NOT describe shape/center/spread/outliers of this

(note): Order of bars doesn’t matter here, so describing how it looks isn’t useful

If asked to describe Categorical Graph:

1. Just describe the different heights of bars between categories and how they compare (what is highest, lowest, etc.)

2. Example: “______ (category with highest bar in bar graph) had the highest probability (or percentage or counts) of _____ (value of highest bar), next was ___________ (category with second highest bar in bar graph)…”

Quantitative Graph: (3 types)

Dot plot (Good for small sample size),

Histogram (Good for medium-large sample sizes),

Box plot (link to 5-number summary)

If asked to describe Quantitative Graph: (must hit all 4 descriptors)

Shape

Center

Spread

Outliers

Description example for Quantitative graph data:

“The distribution of ________ (quantitative variable) is ___________(shape: approximately bell-shaped OR left/right-skewed) with a __________ (center: mean OR median) of _________ (value of mean OR median, WITH UNITS) and a _________ (spread: IQR OR standard deviation) of ___________ (value of IQR OR standard deviation, WITH UNITS). There are _________ (presence of outliers) outliers.”

a. ALERT: Do not mention “center” or “spread” by name, only use name of your choices based on the shape/outliers

b. Summary Stats

Summary Stats (5)

Mean & Standard Deviation

Median & IQR

5-number Summary

Which measures of center and spread are appropriate?

Resistant Statistics

Mean:

Standard Deviation:

Median:

Median = middle value

IQR :

IQR = Q3-Q1

5-number Summary:

(this is going from smallest to largest in quartiles.)

1. Minimum, first quartile, median, third quartile and maximum

2. In JMP output, reported to the right of the histogram

Which measures of center and spread are appropriate?

1. Skew and/or outliers = median and IQR

2. Bell shaped AND no extreme outliers = mean and standard deviation

Resistant Statistics:

1. Median and IQR are resistant statistics, meaning they are better at being unaffected by skewness and outliers