Statistics question

PLAN(NING AHEAD): SAMPLING

VARIABILITY

Biol/Stat 2244 – Peter

Objectives

By the end of this module, you should be able to:

 Identify the inference goal of a study;

 Distinguish between, and categorize data by, type of variables;

 Identify the number of comparison groups in a study;

 Distinguish between matched and independent samples;

 Use vocabulary relevant to selecting possible inference procedures (e.g. matched, independent samples, two-sample, confidence interval, etc.).

Biol/Stat 2244 – Peter

Scientific Inquiry Framework: PPDAC

Problem Define the research question.

Plan Decide how to address the research Problem.

Data Execute your Plan and examine your Data.

Analysis Extract meaning from your Data.

Conclusion Interpret your results in the context of the Problem

(MacKay & Oldford, 2000)

Biol/Stat 2244 – Peter

Plan

Create a plan—including data collection and

analysis—to address the research question(s)

• What is the study population and sampling

strategy?

• What will be measured for the response

variable(s)?

• How will you deal with explanatory variables?

• What statistical procedures do you plan to use?

Biol/Stat 2244 – Peter

Sampling variability

Sampling error

difference between a

statistic and parameter,

due to chance sample

composition

variation in the value of a statistic from sample to

sample

Biol/Stat 2244 – PeterReasonable video explanation of sampling error: https://www.youtube.com/watch?v=uGuWrPFStdg

Statistical Inference

infer

sample population

Forming judgements about

population parameters

and relationships among

variables, on the basis of

sample data

Biol/Stat 2244 – Peter

Inference procedures use knowledge of

sampling variability and/or estimates of

sampling error to help draw conclusions e.g. hypothesis tests, confidence intervals

Describing your data and analyses

Questions that can help identify possible analysis

procedures

• What is your analysis goal?

• How many “samples” or groups are you

comparing?

• Are your data independent or matched

“samples”?

• What type of variables are you analysing?

• What characteristic(s) is/are of interest? Biol/Stat 2244 – Peter

Is Enduron better at reducing blood pressure, on

average, than Diovan in men with hypertension?

Confidence Interval

Hypothesis Test Biol/Stat 2244 – Peter

Some inference procedure ‘goals’

Is Enduron better at reducing blood pressure, on

average, than Diovan in men with hypertension?

Estimate the value of a parameter

Assess evidence against a claim about a

parameter or relationship between variables

Number of “samples”

Does weight gain differ between oral contraceptive (“OC”)

users and IUD users?

Biol/Stat 2244 – Peter

In the context of inference, the term “sample” is generally

interpreted as ‘comparison group’

OC

users

Study 1

IUD

users Females

Study 2

Pop’n

OC users

(n1)

IUD users

(n2)

Females

(n)

Treatment:

OC (n1)

Treatment:

IUD (n2)

OC

users

IUD

users

re p re

se n ts

re p re

se n ts

Structure of data/“samples”

Many statistical procedures require understanding the

structure of the data collected:

Independent samples Matched/paired samples

explicit matches (non-arbitrary)

between responses and/or units Biol/Stat 2244 – Peter

nominal

ordinal

interval

ratio

Values can be ordered

Values can be named

Distance between consecutive

values is constant

Zero means none

Quantitative

Categorical

Biol/Stat 2244 – Peter

Also: discrete or

continuous

Types of variables

Characteristic(s) of interest

The analysis procedure may depend on the

characteristic of interest for the population

• Parameters: mean, median, proportion, variance

• Distribution: Normal, Poisson, …

• Relationship: linear, exponential, …

Biol/Stat 2244 – Peter

Summary

• Statistical analysis should be part of the initial

plan for your research;

• Study design and variable type influence your

choice of analysis.

Biol/Stat 2244 – Peter

Prompt: What are some variables that could be both

categorical and quantitative, depending on the

method of measuring them?

Post to “Thinking about different types of variables”