AP Stat magic terms Unit 1

Population

everyone or everything needed to study or survey in order to answer whatever question we have

purpose

answer questions about populations

sample

subset of your population

descriptive statistics

collecting, summarizing and presenting sample data in a graph/chart

inferential statistics

using a sample to “go beyond” and tell about a population

categorical data

data in the form of categories

numerical data

data in the form of numbers

continuous numerical data

can be measured at whatever decimal level you want (time, lengths, weights)

discrete numerical data

data that isn’t continuous (counts, money(usually))

what chart is used for categorical data?

bar chart

what chart is used for numerical data?

dot plot

where do the actual data values go on an axis of a bar chart?

the bottom

To describe a dot plot (or any plot of numerical data) what do you need to provide?

center, shape, spread, context

what shapes are there?

skewed, left, right, bimodal, mound shape, roughly symmetric

What do you do for center?

Estimate the center. Later, mean and median! Also include context with it.

Spread?

Give the range (high minus low)

What should you do with two data sets?

COMPARE THEM (centers, shapes and spreads)

How to compare?

lower than, more spread out than, etc.

what are the two types of studies?

observational and experiments

what do you do in an observational study

go out and collect data

what is the goal in an experiment

to determine if there’s a cause and effect relationship of an explanatory variable on a response variable

How do you do an experiment?

By RANDOMLY ASSIGNING the experimental units to different treatment groups where you will apply the explanatory variable to each group to see if there is a difference in the response variable among the treatments. 

Explanatory variable

the variable causing the difference in treatments. The possible values of the treatment (it explains the variation between the groups)

Response variable

the variable you are measuring at the end, to see if there is a difference. The possible values of the result that you are measuring

Experimental units

the things or people that are randomly assigned to treatment groups

Random selection (random sampling)

when you select subjects from the population “at random.” Everyone has an equal chance of being picked

How to create a random sample of 50 people from a list of 2000?

Use a hat! Put all 2000 names in a hat, shake the hat, and pull out 50. They are your subjects

Random assignment (randomization)

Done in experiments only. It’s when we randomly put our already-selected subjects into our different treatments.

What is the purpose of random selection? (Magic phrase)

To create a sample that is representative of the population.

What is the purpose of random assignment?  (Magic phrase)

To create treatment groups that are roughly equal on extraneous variables, so that the only difference between them is the explanatory variable (or treatment).

Simple random sampling (SRS)

In an SRS, you get every possible name from your population, and you simply choose n in some random way from the list.

Stratified random sampling

If the population is naturally split into subgroups, and you want to make sure all groups are represented proportionally, sample from each group separately.  These groups are called strata.

Ideally you would sample from each proportionally, but it’s not required.

Cluster sampling

When you pick an entire group at random rather than individuals.  You can only do this if you are sure the group will be representative of your population.

Systematic sampling

When you pick the first person from a list at random, then choose every k^th person after that. (Ex. every 4th person on a list of 200)

Convenience sampling

When you pick whoever is nearby and easy.  Or pick your friend.  Or take only those who call in, or only those who log into your website.  It doesn’t make a representative sample, and it makes me unhappy.

Bias

Even if you do random selection (random sample) correctly, bad things can still happen to mess up your sample. Sometimes it’s your fault, sometimes not. In general, bias is a tendency for samples to differ from the population in some consistent way.

Selection bias

When you systematically exclude a part of the population.

Example:  Phone surveys exclude those without phones, generally homeless.

Measurement bias (or response bias)

When how you collect the data is a problem

Example: Asking “knowing that smoking causes lung cancer, how do you feel about smoking?”

 Nonresponse bias

When you don’t get responses from the sample you select.

Example: When you mail out surveys, and you only get a 40% response rate.

Treatments

The different experimental conditions being compared

Explanatory variable

Replication

Using more than one subject or observation for each treatment group.

Direct control

Variables that the experimenter directly manipulates or controls. 

What is the goal of direct control? (Magic phrase)

The goal is to reduce variability so that differences can be more easily seen.

Control group

When one experimental group receives no treatment. Not every experiment needs a control group! You only do this if your experiment is comparing one treatment (like a new drug) to nothing (like no drug).

Confounding variable

A variable related to (in between) both the explanatory variable and the response variable.  If you have it, you can’t tell if treatment effects are due to treatment or a different factor. Rare in a well-designed experiment