Statistical Statistical ReasoningReasoning

Chapter 1, Lecture 3Chapter 1, Lecture 3

“To be an educated person today is to be able to applysimple statistical principles to everyday reasoning.One needn’t memorize complicated formulas to thinkmore clearly and critically about data.”

- David Myers

Statistical ReasoningStatistical procedures analyze and

interpret data allowing us to see what the unaided eye misses.

Composition of ethnicity in urban locales

Statistical Reasoning in Everyday Life

Doubt big, round, undocumented numbers as they can be misleading

and before long, become public misinformation.

Apply simple statistical reasoning in everyday life to think smarter!

Describing DataA meaningful description of data is

important in research. Misrepresentation may lead to incorrect conclusions.

Measures of Central Tendency

Mode: The most frequently occurring score in a distribution.

Mean: The arithmetic average of scores in a distribution obtained by adding the scores and then dividing by the number of scores that were added together.

Median: The middle score in a rank-ordered distribution.

Measures of Central Tendency

A Skewed Distribution

Measures of Variation

Range: The difference between the highest and lowest scores in a distribution.

Standard Deviation: A computed measure of how much scores vary around the mean.

Standard Deviation

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Normal Curve

A symmetrical, bell-shaped curve that describes the distribution of many types of data (normal distribution). Most scores fall near the mean.

Remember the 68-95-99.7 rule???Remember the 68-95-99.7 rule???

Illusion of Control

1. Illusory Correlation: the perception of a relationship where no relationship actually exists.

2. Regression Toward the Mean: the tendency for extremes of unusual scores or events to regress toward the average.

That chance events are subject to personal control is an illusion of control fed by:

Making Inferences

A statistical statement of how frequently an obtained result occurred by

experimental manipulation or by chance.

Making Inferences

1. Representative samples are better than biased samples.

2. Less-variable observations are more reliable than more variable ones.

3. More cases are better than fewer cases.

When is an Observed Difference Reliable?

Making Inferences

When sample averages are reliable and the difference between them is relatively large, we say the difference has statistical significance. It

is probably not due to chance variation.

For psychologists this difference is measured through alpha level set at 5 percent.

When is a Difference Significant?

Interesting Statistical Facts

Given any two people in the United States, how manyintermediaries are necessary, on the average, beforethe two are in communication, assuming that theintermediaries may only contact people they know ona first-name basis? 5 people

Imagine a huge piece of paper about the thickness ofone textbook page. If it were folded in half 50 times,how thick would it be?About 50,000,000 miles

Interesting Statistical Facts

Assuming a world population of about 6.5 billion, ifwe gathered everyone together and allotted eachperson a generous two-by-two feet of ground, howlarge an area would we need?

About 933 square miles, considerable less thanRhode Island’s 1545.

What if we allowed everyone to sit comfortably in216 cubic feet (6 feet on a side)?

Every human being on earth would fitcomfortably into the Grand Canyon.

HomeworkRead p.38-43

Now let’s practice calculating some ofNow let’s practice calculating some ofour own statistics from the data gatheredour own statistics from the data gatheredon Handout 1-12…on Handout 1-12…