Exam 2 Lecture 4

Question 1

Population=

Answer 1

Everyone

Question 2

Parameter=

Answer 2

What you want to know about a population

Question 3

A part of a population=

Answer 3

A sample

Question 4

What you can compute from a sample to estimate a parameter

Answer 4

Statistic

Question 5

How good a statistic is depends on how good _______

Answer 5

Your sample is

Question 6

How likely your statistic (estimate) actually reflects your parameter

Answer 6

Accuracy

Question 7

A __________ is a parameter estimate

Answer 7

Statistic

Question 8

Since your can’t measure everyone, you __________ a _________ by using a ___________

Answer 8

Estimate a parameter by using a statistic

Question 9

One of the main objectives of statistics is to estimate information about everyone from a smaller group. This is a ________

Answer 9

Sample

Question 10

To pick a sample, you need to ask yourself:

Answer 10

• What is the parameter I am interested in?
• What is the population? (in stats, the population isn’t always 8 billion)

Question 11

Picking a sample isn’t as easy as it looks! For statistics to work, the sample you select must be ________________. That means your sample must match your population in every way possible so it is more likely to truly reflect all the different people in a population.

Answer 11

Representative

Question 12

Which population are we a good sample of?

Answer 12

• All of humanity?
• Americans?
• New Jerseyans?
• American college students?
• Rutgers students?
• STEM-focused college students?
• Exercise Science majors at Rutgers?

Question 13

What would be a good vs. bad sample for Americans?

Answer 13

Bad sample: Middle-aged white moms from New Jersey and Florida

Good sample: A few randomly selected people from every zip code in US

Question 14

What would be a good vs. bad sample for Division 1 athletes?

Answer 14

Bad sample: Rutgers football players

Good sample: A few athletes from various sports from all D1 schools in US

Question 15

Not just who, but how. Maybe you know who a good sample is, but how do you find them?
You need a strategy for picking people -> sampling procedure.
This strategy must be fair and impartial.

When do statisticians make mistakes during sampling procedure?

Answer 15

Statisticians make mistakes when there is a SELECTION BIAS (a consistent habit of excluding one kind of person).

EX:
Parameter: Next president
Population: US Citizens
Q: Who will win the next presidential election?
- If you ask people from, Texas only… California only
- If you ask people age 18-22… 75-80
- If you ask people from cities… or rural communities

ALL are forms of selection bias

Question 16

What is selection bias?

Answer 16

A consistent habit of excluding one kind of person

Question 17

Maybe you ASK a good sample, but do they respond?
- You need to remember that not everyone is going to answer. In fact, non-response is very common!
- Often a statistician/scientist will sample 10,000 to get 1,000 responses

What kind of bias could you encounter in this scenario?

Answer 17

Non-response bias.

Excluding a group (not because you didn’t ask) but because you asked in a way they weren’t interested in (your sampling procedure)

Q: Who will win the next presidential election?
- If you MAIL a paper survey that needs to be mailed back?
- If you make a TIKTOK and ask for comments?
- If you stand in a mall and approach people?

Responders and non-responders will be different.

In general, the lower-income and upper-income people respond less than middle-income people. This can be a problem.

Question 18

Sample size (about)

Answer 18

• More is not always better (but less is often a problem!)
• Your sample must be big enough to represent the population, so a bigger/more varied (heterogeneous) population will need a bigger sample (Ex: People aged 25-30 (millions) vs. Rutgers juniors (thousands)
• Sometimes a sample size is decided by what is statistically the best, sometimes it is decided by what is feasible (Ex: You have 2 weeks to collect data vs. 2 years. Or $2 vs. $2,000,000. A 5-minute survey vs. a 5-hour experiment)
• There are statistical tools to determine a good sample size

Question 19

Group B’s value is certainly larger BUT does this mean that everyone would build muscle faster by working out in the evening?

What is the sample, population, parameter, and parameter estimate?

Answer 19

Sample: Group B
Population: Everyone
Parameter: Build muscle
Parameter estimate: Value

Question 20

Sampling is the core of statistics. Is the difference in the example of skeletal muscle greater than ‘chance’ (just random noise) or would that difference hold up if we actually measured everyone? How good is your sample? What do you need to ask to determine?

Answer 20

Does my sample reflect the whole population?

Question 21

In order to say anything reliable/valid/accurate/stable/reproducible about a population…
You need what?

Answer 21

1. You need a good protocol
   - It must be detailed and consistent
   - It must control for outside influences that can mess things up (Asking about illegal drug use? Don’t have a police officer standing behind them!)
2. You need a good sample
   - To be a good sample, it needs to truly represent the population

If you do these things, you will get good data.
- It is possible to collect good-quality objective and subjective data (but it’s also obviously possible to collect junk)