Basic Statistical Questions Are two (or more) groups different? - - PowerPoint PPT Presentation

Basic Statistical Questions

Are two (or more) groups different?

Does feed type affect weight? Do different feed types affect survival rates? Are spotted pigs faster than non-spotted pigs?

Basic Statistical Questions

Is there a relationship between a dependent and one or more independent variables?

Independent variable: A variable that can be manipulated by a researcher, or varies naturally without human intervention. Often called a treatment or a dose. Dependent variable: A variable that responds to or may respond to one or more independent variables. Often called response.

Basic Statistical Questions

Questions one might ask: Is there a relationship between the water temperature in the bay and the concentration of viruses? Is there a relationship between Providence River flow rates and phosphate concentrations in the upper bay?

Population vs. Sample

• Population: every individual of a particular

group that exists anywhere in the universe.

• Sample: a subset of the population on which

some measurement/study is conducted.

Experimental units and replication

Consider a statistical question: Are two groups different? Consider average tail length on: Irish Wolfhounds Some fuzzy rat dog Compared to:

We need a sample of each population

Replicate or Experimental Unit: The smallest unit to which a treatment (or measurement) is independently applied.

Could we be wrong?

Results?

• Can you guess what the results of the tail-length study might

be?

• Is that really what we want to evaluate?

Types of Data

• Ratio
• Most data that you see will probably be here
• Anything that can be “twice” or “half” as much (lengths,

weights, speeds etc.)

• Constant interval size (linear change, not log).
• Physically meaningful zero point. Not a human-dictated

arbitrary zero.

• Interval
• This is almost like Ratio data, but there is no physically

meaningful zero point.

• Temperature in °C and °F fall into this category. How about

K?

• What about time?
• What about latitude and longitude?
• Still need a constant interval.

Types of Data

• Ordinal
• As in “in order”
• We might have an order without actual numbers. (e.g. letter

grades)

• It may not be possible to measure exactly
• Or, the statistical evaluation might require that ordinal data

be used, even if exact measurements are available (more on that later).

Types of Data

• Categorical (also called Nominal)
• As in “categories” or “names”
• Genetic phenotypes (e.g. brown hair, green eyes, etc.),

taxonomy, etc.

• Basically, anything that can be used to define a group.
• Consider our basic question: Are two or more groups

different? Categorical variables define the groups.

Types of Data

• For Ratio and Interval Data the data can be,
• continuous- any value is possible
• discrete- the possible values move in steps. For

example, age in years.

Types of Data

In JMP

Categorical/Nominal Ratio/Interval Ordinal Note: JMP does not seem to differentiate continuous from discrete directly. But appears to treat discrete as

• rdinal.

What about the following?

• 1. Number of Right Whale calves observed in 2014
• 2. Clown fish diet type
• 3. Water salinity
• 4. Shoe sizes
• 5. Root/Shoot mass

Ratio, Interval, Ordinal, Categorical, Continuous, Discrete?

• What data should I collect?
• What is your hypothesis?
• What statistical tests will you be using?
• How willing are you to be wrong (statistical power is

determined by the sample size)?

• In addition to your specific hypothesis, are there other

variables (both dependent and independent) that might play a role? If so, you better measure them now, because it’s unlikely you will be able to go back.

• What have other studies done? Are their data well behaved

(e.g. normal distribution/bell curve)

Basic Statistical Questions