Data Production

Data Production Slide #2

Two General Methods for Collecting “Proper” Data

• Observational (or sample-based)• Experimental

Data Production Slide #3

Illustrative Example• A world-famous chipmunk biologist• Interested in the effect of temperature

on digestive rate

Manitoba Ashland OzarksTemp 16.9 19.1 22.1

DigRate 0.145 0.168 0.195

ObservationalStudy

Temp 18 20 22DigRate 0.152 0.173 0.187

ExperimentalStudy

Can we conclude that increases in temperature CAUSED increases in digestive rates?

What is the fundamental difference between an observational and experimental study?

Data Production

What are at least three situations where an observational study would be valuable even if cause-and-effect statements can not be made?

Slide #4

Data Production Slide #5

Types of Observational Studies• Voluntary Response

– Individuals choose their self for the sample by responding to a general appeal

• Convenience– Gather individuals that are easiest to reach

• Any problems with these two methods?– Biased sample – a sample where a segment of

the population is systematically favored

Data Production Slide #6

Types of Observational Studies

• Convenience

• Voluntary Response

• Probability-based– Each individual has a known chance (probability)

of being selected for the sample– Most common is Simple Random Sample (SRS)

Data Production Slide #7

How to Select a SRS1) Assign a unique number to each individual in the

population

2) Select n random numbers (without replacement) from between 1 and N

• Numbers on ping-pong balls and draw• Random number table• Computer generated

3) Gather individuals that correspond to the selected numbers

Population Size

Data Production

What type of study are the following?– A researcher is interested in the makes of cars found in

Ashland. She sits at the corner of Ellis and Hwy 2 and records the makes of cars that are driven by.

– A researcher is interested in the makes of cars found in Ashland. She calls a random sample of Ashland phone numbers and asks the respondents if they will take her survey. If they do, she records the make of car they own.

– A researcher is interested in the makes of cars found in Ashland. She collects a sample of car registrations for Ashland owners from a statewide database such that each registration had the same chance of being selected.

Slide #8

Data Production

What type of study are the following?– The manager at Burger King is interested in customer

satisfaction. To get a handle on this he provides each customer with a short survey card to be completed and returned to a collection box on the front counter.

– A wildlife manager needs to determine the sex ratio of deer in northern Wisconsin. Towards this end, he records the sex of road-kill deer from along Hwy 2.

Slide #9

Data Production Slide #10

Random Samples are Required

• Because ...– … they remove bias (provide representation)– … allow the laws of probability to be used

(inferences can be made)

Data Production

How would you take a random sample of …….. Lake Trout from Lake Superior?

….. Red Oak trees from northern Wisconsin?

….. people from Wisconsin?

Slide #11

Data Production Slide #12

Experimental Design• Example found 30 similar chipmunks to be

split into three groups -- 18, 20, 22oC. Control all other variables and measure digestive rate.

Data Production Slide #13

Definitions in Experiments• Response - variable of interest, not controlled

– Example --> digestive rate

• Factor (aka, explanatory variable) - variable controlled at different values– Example --> temperature

• Levels - number of values of each factor– Example --> 3 (18, 20, 22oC)

• Treatments - number of different conditions in expe– Example --> 3

• Replicates - number of individuals in each treatment– Example --> 10

Data Production Slide #14

• Response - variable of interest, not controlled– Example --> digestive rate

• Factors - variables controlled at different values– Example --> temperature, food type

• Levels - number of values of each factor– Example --> 3 (18, 20, 22oC); 2 (corn, sunflower seeds)

• Treatments - number of combinations of all factors– Example --> 6

• Replicates - number of individuals in each treatment– Example --> 5

A Modification -- Also want to simultaneously assess the effect of food type (corn, sunflower seeds) on digestive rate.

Data Production Slide #15

FoodTypeCorn Sunflower

18Temp 20

22

Diagram of 2-factor Experiment

3,4,5,26,10 13,20,16,17,1511,2,27,29,7 23,12,18,21,830,9,6,25,14 28,1,24,19,22

Data Production

A student is designing an experiment to determine the simultaneous effects of calcium in the diet and regular exercise on blood pressure. Some subjects will be given a calcium supplement pill and some will be given a placebo pill. In addition, some subjects will be required to perform aerobic exercises once a day, whereas others will not. The researcher has 32 male subjects available that are as similar as possible (similar ages, weights, initial blood pressures, etc.).

• What is an individual?• Identify the response variable, factors, levels, treatments,

and replicates.Slide #16

Data Production Slide #17

Principles of Experimental Design

• Control -- control all variables except the response variable

• Randomization -- randomize the allocation of individuals to control for bias and allow the laws of probability to be used

• Replication -- use multiple individuals in each treatment to control for natural variability and the effect of outliers