Welcome to Statistics

Chapter 1Terminology

Basic terms to be familiar with

Statistics – the study of how to collect, organize, analyze and interpret numerical information from data.

Descriptive Statistics: Organizing, picturing and summarizing information

Inferential Statistics: Using information to draw conclusions

Basic Terms (cont)

Individuals – people/objects in the study (nouns)

Variable – Characteristic of the individual to be measured/observed

Quantitative – value/numerical

Qualitative – descriptive, allows for categorizing

Basic Terms (cont)Population Data: From every individualSample Data: From some individualsIncomplete Population: open ended

populationData Types

Nominal – names, labels, categoriesOrdinal – basic ordering of data - comparableInterval – order + differences have meaning

(class rank)Ratio – order + interval + true “zero” exists

(GPA)

Lets do an activity

Record your pulse 3 times. I will give you a start and stop.

Is this data quantitative or qualitative?

How could we organize this data?What could we find? Lets find the average

pull rate of the females and then the average pulse rates of the males

1.2 How do you choose individuals?

Census: Use of measurements from entire population

Sample: Use of measurements from a representative part

Random Samples

Simple Random Sample: a sample of a population that, on average, looks like the rest of the population. That is, it is a subset such that

a) Every sample has an equal chance of being selected and

b) Every member of the population has an equivalent chance of being in the sample

(cont)

Stratified Sampling: a population is divided into strata (common characteristic subsets) and a random sample of certain size is drawn from each.

Systematic Sampling: members of population are sequentially numbered. From any particular starting point, every kth member is included in the sample

(Odds, evens, etc)

(cont)Cluster Sampling: A population is divided into

“clusters” (geographic). Clusters are randomly selected and every member of a cluster is included in the sample

Convenience Sampling: including those who are convenient (i.e. readily available). This could create bias

Voluntary Response Sample: large group is asked ot respond; those who do are counted.

Undercoverage: A portion of the population is not sampled or has a smaller representation in the sample than it is in the population

¼ of US = Seniors, but if ¼ of sample isn’t seniors, that is considered undercoverage.

(cont)

Random Number Table: A way to generate random numbers.

Calculators and computers can randomly generate numbers.

Lets see how this works:

Random Number Table1 96299 07196 98642 20639 23185 56282

69929

2 71622 35940 81807 59255 18192 08710 80777

3 03272 41230 81739 74797 70406 18564 69273

4 47376 58596 14365 63685 56555 42974 72944

5 47352 42853 42903 97504 56655 70355 88606

6 20064 04266 74017 79319 70170 96572 08523

7 73184 95907 05179 51002 83374 52297 07769

8 72753 36216 07230 35793 71907 65571 66784

(cont)

Simulation: numerical representation that models a situation. “Dry Lab”

Component: most basic event; has a randomly occurring outcome. Think about selecting a box of cracker jacks and each box has a prize.

Trial: The sequence of eventsWhat happens in the trial is called the

response variable.

1.3 Experimental Design

Observational Study – measurements don’t change response or variable

Experimental Study – “treatment” is deliberately imposed and results are observed

This may include a control group which allows for a baseline measurement. Control group receives no treatment.

(cont)

Placebo effect – subject gets no “treatment” but believes that h/s is and responds favorably. The placebo is a “fake” treatments looks like the real treatment.

Double blind – neither the individual nore the observers are aware of which group receives the placebo.

One patient stands out in the memory of Stephen Straus, M.D., for her remarkable recovery, more than 10 years ago, from chronic fatigue syndrome. The woman, then in her 30s, was "very significantly impaired," says Straus, chief of the Laboratory of Clinical Investigation at the National Institute of Allergy and Infectious Diseases. "She had no energy, couldn't work, and spent most of her time at home." But her strength was restored during a study to test the effectiveness of an experimental chronic fatigue drug.

"She and her parents were so thrilled with her recovery that they were blessing me and my colleagues," recalls Straus, the principal investigator on that study.

http://www.fda.gov/fdac/features/2000/100_heal.html

Like many drug studies, the chronic fatigue medication trial was a "placebo-controlled" study, meaning that a portion of the patients took the experimental drug, while others took look-alike pills with no active ingredient, with neither researchers nor patients knowing which patients were getting which.

It's human nature, Straus explains, for patients and investigators alike to try and guess in each case: Is it the real drug or a dummy pill? But people shouldn't kid themselves, he says, that they can consistently tell the actual drug from the sham by seeking out tell-tale signs of improvement.

http://www.fda.gov/fdac/features/2000/100_heal.html

Turns out, the woman's quick turnaround from chronic fatigue occurred after taking placebo pills, not the experimental drug. Straus says, "She was amazed by the revelation that she'd gotten better on placebo."

Research has confirmed that a fake treatment, made from an inactive substance like sugar, distilled water, or saline solution, can have a "placebo effect"--that is, the sham medication can sometimes improve a patient's condition simply because the person has the expectation that it will be helpful. For a given medical condition, it's not unusual for one-third of patients to feel better in response to treatment with placebo.

http://www.fda.gov/fdac/features/2000/100_heal.html

How do you Design a study?1. Identify individuals/objects of interest2. Specify variables (response)3. Specify treatments, protocols, controls and

assignments4. Determine whether census or sampling5. In the plan, address ethical, confidentiality and

privacy issues. Obtain permission if necessary (school survey, etc)

6. Collect Data7. Observe or infer8. Note concerns about data collection and make

future study recommendations.

Some Ways to Gather Data

1. Survey – Yes/No response2. Rated Response – 1 to 5 scale type

responses are what is called a Likert Scale.

3. Open ended response – researcher must in some way categorize answers.

Pitfalls in Gathering Data

Conscious/Unconscious biasTruthfullness of respondees?Is the sample a true representation of

the population?Non-responseVoluntary response samples (self-

selecting) may over-represent those with strong opinions.

Lurking vs confounding variables

Confounding variables – associated in a “non causal way” with a factor, and affects response.

Cornell ProfessorLurking Variables - unknown/ unanticipated

variables that may be an underlying cause for observed change in response. Perhaps forgotten….

TV sets vs life expectanciesControl groups can help observe and identify lurking

and confounding variables.Some books do not distinguish between the two