module 1: application of statistics & data definitions

Statistics?

The science of data: collect, organize, analyze, interpret

Data?

Things you collect info about (plural; singular is datum)

Data set?

A table of all the data for one study

Element?

One individual thing in the data set (one row's subject)

Observation?

All the data collected for one element (the full row)

Variable?

A measurable characteristic (a column), like age or income

Why use a unique ID for each element?

Elements can share names (two John Smiths)

Qualitative data?

Describes something (category); can be numbers or words

Quantitative data?

How much / how many; always numbers; math makes sense

Quick test for quantitative?

Does averaging it make sense? Yes = quantitative

Numbers that are NOT quantitative?

Student ID, zip code, SSN (they are labels)

Cross-sectional data?

Snapshot: one point of reference

Time series data?

Same thing measured over many time periods

Cross-sectional or time series test?

Different things at one moment = cross-sectional. Same thing over time = time series

Descriptive statistics?

Summarizes the data you already have

Most common numerical statistic?

Average (mean)

Population?

The whole group you care about

Sample?

The smaller group you actually study

Inferential statistics?

Uses a sample to make conclusions about the population

Descriptive vs. inferential?

Describe what you have vs. generalize beyond it

Why use a sample?

Studying everyone costs too much time and money

Purpose of Campus variable?

Checks if location influences the element

Purpose of Class and Major?

Compare groups (apples to apples)

4 levels of measurement?

Nominal, Ordinal, Interval, Ratio (NOIR)

Nominal?

Names or labels only; no math

Ordinal?

Can be ranked; differences not meaningful

Interval?

Ordered, differences meaningful, no true zero

Ratio?

Interval plus a true zero; "twice as much" works

Inherent zero?

A zero that means "none"

Interval vs. ratio test?

Does "twice as much" make sense? Yes = ratio

Level of measurement ladder?

Category = nominal. Order = ordinal. Differences = interval. Ratios = ratio

Temperature (°F or °C) level?

Interval

Money, rainfall, counts level?

Ratio

Point of reference in cross-sectional data?

A time, date, or point in space

Two ways to gather research data?

Use existing data, or collect it yourself

3 sources of existing data?

Organization records, free sources, purchased data

Two types of statistical studies?

Experimental and observational

Experimental study?

Researcher changes (manipulates) variables

Observational study?

Researcher only watches, changes nothing

Passive observation?

No interaction with subjects

Active observation?

Some interaction (survey, questionnaire, focus group)

Experimental or observational test?

Did the researcher manipulate a variable? Yes = experimental

Two principal methods of data collection?

Simulations and surveys

Simulation?

Using math or physical models (often on a computer) to reproduce a situation or process

Why use a simulation?

Cheaper, faster, and safe for situations that are dangerous or impractical in real life

Survey?

Asking questions to investigate one or more characteristics of a population

Main rule for survey questions?

Word them so the responses are unbiased

Ways to deliver a survey?

In person, phone, Internet, or mail

Erroneous vs. omitted data?

Erroneous (wrong) data often hurts a study more than omitted (missing) data

Examples of data errors?

Transposed numbers; a respondent misunderstanding a question

Outlier?

A value that is out of place: much too small or too large

Before using data, what must a statistician do?

Vet the data source and the collection method

Existing data example from the bakery case?

Government websites for population demographics

Counting customers each day: what type of study?

Observational (just watching, changing nothing)

Changing recipe ingredients to test sweetness: what type of study?

Experimental (manipulating variables)

3 key elements of a well-designed experiment?

Control, randomization, replication

What can ruin an experiment?

Too many treatments, no controls, too small a sample

Confounding variable?

You can't tell which factor caused the effect (fatigue vs. boredom)

Placebo effect?

A subject reacts favorably to a fake treatment

How do you control the placebo effect?

Blinding

Blinding?

Subjects don't know if they got the treatment or the placebo

Double-blind?

Neither subjects nor experimenter know (preferred design)

Randomization?

Randomly assigning subjects to treatment groups

Completely randomized design?

Subjects assigned to groups purely by random selection

Block?

A group of subjects with similar characteristics

Randomized block design?

Divide into blocks, then randomly assign within each block

Matched-pairs design?

Pair similar subjects; randomly pick one for treatment, other is control

Problem with a too-small sample?

May be biased or invalid

Problem with a too-large sample?

Data is hard to process

Replication?

Repeating the experiment under the same or similar conditions

Trial?

One run of the experiment

Census?

A count or measure of the entire population

Sample (count or measure)?

A count or measure of part of the population

Why is a census rarely used?

Difficult and costly

What makes a sample unbiased?

It is representative of the greater population

Can sampling errors happen in a well-designed study?

Yes

Random sample?

Every member of the population has an equal chance of being selected

Simple random sample?

Every possible sample of the same size has an equal chance of being selected

Random vs. simple random sample?

Random = equal chance for each member. Simple random = equal chance for each possible sample of the same size

How to collect a simple random sample?

Assign each member a number, then pick numbers with a random number table or generator

Using a random number table: how many digits at a time?

As many digits as the largest number in the population (500 students = 3 digits)

Random number too high for the population?

Skip it and go to the next number

Selection with replacement?

The same person can be chosen more than once

Selection without replacement?

The same person can NOT be chosen more than once

Stratified sample?

Divide into strata (shared trait), then sample from EVERY stratum

Stratified sample rule?

Sample each stratum in proportion to its share of the population

Cluster sample?

Divide into clusters, then take ALL members of one or more (not all) clusters

What is the risk with a cluster sample?

A cluster may not represent the whole population (e.g., one high-income zip code)

Systematic sample?

Random starting number, then every kth member

When should you avoid systematic sampling?

When the data has regular patterns

Convenience sample?

Members who are easy to obtain (e.g., people stopped at a mall)

Stratified vs. cluster?

Stratified = some from EVERY group. Cluster = EVERYONE from SOME groups

Descriptive statistics (1.5 definition)?

A compiled summary of the data analysis

3 forms of descriptive statistics?

Tabular, graphical, numerical

Frequency?

How many times a value occurs (the count)

Percentage in a frequency table?

Frequency divided by the total, times 100

What do the frequencies in a table add up to?

The total number of data values

What do the percentages add up to?

100%

Pie chart shows?

Each category's share (percentage) of the whole

Bar chart shows?

The count (frequency) of each category by bar height