Merced College; Don Power

Lecture Notes: Triola, Chapter 1: Introduction to statistics

1.2 Statistical Thinking

Know these definitions:

population	parameter Data relating to an entire population are called parameters
sample	statistic Data from samples are called statistics

Census vs sample

discrete data Can you count it? How many students....

continuous data Can you get fractional measurements? Average speeds of ..

voluntary response sample – Why would such samples cause studies to go wrong?

1.3 Types of Data

The point: Don't use methods/computations that are inappropriate for your type of data.

Know the four types of data: First 2: Qualitative, Last 2: Quantitative

Nominal - Based on names

e.g. male, female

or, far west, midwest, southern, mid-atlantic, northeast

Ordinal - Some order is possible, even if it can't be quantified

e.g. large, medium, small

or, child, adult, senior

Interval - Numerical scales (like temperatures); ratios are not valid

e.g. songs from the 50's, 60's, 70's, 80's, ...

Ratio - Numerical ratios can be formed and are valid

(Test: if you double one number, are you also doubling the quantity you are measuring? Is 60 degrees twice as warm as 30 degrees? Is 60 pounds twice as heavy as 30 pounds?)

Question: What type is appropriate for the numbers on football jerseys? (The bigger the player, the bigger the number?)

1.4 Critical Thinking

Per text, main sources of errors in statistical work:

Dishonesty (on the part of the researcher or the people providing the data)

Unintentional errors (Are political polls always accurate?)

Did you get a valid sample?

Did you draw a valid conclusion from your sample?

Good sampling techniques are crucial. Potential errors could come from:

Voluntary response sample (or self-selected sample)

Samples that are too small

Loaded questions: questions worded in a way that affects the response

Order of the questions, or the order of the phrases in the questions

Nonresponse

Missing data

Self-interest study

Other errors relate to presentation of the results

Misleading graphs or pictographs

Errors interpreting percentages – Text has a good summary of % calculations

Confusing correlation with causality

Overly precise numbers

Partial pictures

Deliberate distortions

What was the problem with the Literary Digest poll (chapter problem, pg 3)?

Discuss the statement, "90% of all statistics are made up on the spot."

1.5 Collecting Sample Data: “Design of Experiments”

Observational studies vs Experiments

Obsv -- We observe and measure, but don't modify the subjects

retrospective (Past data)

cross-sectional (i.e. current status)

prospective (longitudinal) Future data

Experiment -- we apply some treatment, then observe the effects

Avoid confounding: multiple causes could produce the effect you"re measuring

Be able to distinguish among Sampling strategies (fig 1-2, pg 29)

Random sample -- Each individual member has an equal chance of being selected

Simple random sample -- Every possible sample of size n has the same chance of being selected (If n=1 only, this is a random sample)

Systematic sample – After some random starting point, select every kth member.

Stratified sampling – Subdivide population into subgroups sharing common characteristics (e.g. Democrat, Republican, Independent), and get a random sample within each group

Cluster sampling – Divide population into groups/clusters/classes, select random groups, survey all the members of the selected groups.

Controlling the effects of variables

Blinding -- Hawthorn effect

Blocks -- Sampling strategy.

Fig 1.4:

Randomized block design

Form blocks with similar characteristics

Randomly assign treatments to the subjects in each group

Completely randomized Experimental Design

No blocks

Assign to groups randomly

Rigorously controlled design

Careful selection of subjects: [more thorough consideration of blocks]

"Repetition of an experiment on sufficiently large groups of subjects is called replication"

The idea is to be able to apply the scientific method: if you repeat the experiment you should get the same result

Multistage sample design: combination of sampling techniques

Be able to distinguish among (based on when the data occurred):

Retrospective study

Cross-sectional study

Prospective (longitudinal) study

See decision tree on pg 31: Triola has a number of these: helpful for complex decisons

Return to:  Merced College; Don Power               Updated 08/18/09 by Don Power