Name that tune

R.G. Bias | [email protected] |

Name that tune.

Song title? Performer(s)?

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Scientific Method (continued)

“Finding New Information”3/29/2010

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Objectives I want to arm you with a scientist’s skepticism,

and a scientist’s tools to conduct research and evaluate others’ research.

Swoopin’ out of “scientific method” and “experimental design” and into “statistics.”

- Randolph – remember to take roll.

R.G. Bias | [email protected] |4

Critical Skepticism Remember the Rabbit Pie example

from earlier? The “critical consumer” of statistics

asked “what do you mean by ’50/50’”?

Let’s look at some other situations and claims.


Company is hurting. We’d like to ask you to take a 50%

cut in pay. But if you do, we’ll give you a 60%

raise next month. OK?

Problem: Base rate.


Sale! “Save 100%”

I doubt it.


Probabilities “It’s safer to drive in the fog than in the

sunshine.” (Kinda like “Most accidents occur within 25 miles of home.” Doesn’t mean it gets safer once you get to San Marcos.)

Navy literature around WWI:– “The death rate in the Navy during the

Spanish-American war was 9/1000. For civilians in NYC during the same period it was 16/1000. So . . . Join the Navy. It’s safer.”


Are all results reported? “In an independent study [ooh,

magic words], people who used Doakes toothpaste had 23% fewer cavities.”

How many studies showed MORE cavities for Doakes users?


Sampling problems “Average salary of 1999 UT grads –

“$41,000.” How did they find this? I’ll bet it

was average salary of THOSE WHO RESPONDED to a survey.

Who’s inclined to respond?


Correlation ≠ Causation Around the turn of the 20th century,

there were relatively MANY deaths of tuberculosis in Arizona.

What’s up with that?


Remember . . . I do NOT want you to become

cynical. Not all “media bias” is intentional. Just be sensible, critical, skeptical. As you “consume” statistics, ask

some questions . . .


Ask yourself. . . Who says so? (A Zest commercial is unlikely to

tell you that Irish Spring is best.) How does he/she know? (That Zest is “the

best soap for you.”) What’s missing? (One year, 33% of female

grad students at Johns Hopkins married faculty.) Did somebody change the subject?

(“Camrys are bigger than Accords.” “Accords are bigger than Camrys.”)

Does it make sense? (“Study in NYC: Working woman with family needed $40.13/week for adequate support.”)


We run an experiment . . . to try to see if two (or more) levels of

an IV differentially influence a DV. We hope to find a difference. Finding NO difference can mean one

of two things:– Truly there’s no difference.– Our test – our experiment – just wasn’t

good enough, or sensitive enough, to detect the difference.

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Notice Many things influence how easy or

hard it is to discover a difference.–How big the real difference is.–How much variability there is in the

population distribution(s).–How much error variance there is.– Let’s talk about variance.


Sources of variance Systematic vs. Error

– Real differences– Error variance

What would happen to the DV if our measurement apparatus was a little inconsistent?

There are OTHER sources of error variance, and the whole point of experimental design is to try to minimize ‘em.

Get this: The more error variance, the harder for real differences to “shine through.”


Role of Data Analysis in Exps.

Primary goal of data analysis is to determine if our observations support a claim about behavior. Is that difference really different?

We want to draw conclusions about populations, not just the sample.

Two different ways – statistics and replication.


And so . . . . . . we make the transition to

statistics!! (Yay!)

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How to talk about a set of numbers

We can list ‘em.– Can get WAY unwieldy.– Plus hard to make any sense out of

them. First step – put ‘em in order. Second step –– Graph ‘em, and/or– Calculate percentiles/deciles


Frequency Distributions -Histograms

# of pets ever owned– 13– 2– 1– 4– 0– 1– 3– 0– 5– 1

Put ‘em in order– 0– 0– 1– 1– 1– 2– 3– 4– 5– 13


Freq Dist Raw Scores

(in order)– 0– 0– 1– 1– 1– 2– 3– 4– 5– 13

Raw Score Freq Cumu Freq0 2

21 3

52 1

63 1

74 1

85 1

913 1

10


Histogram

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 13

# of pets


Percentiles LOCATION of 25th percentile:

– X.25 = (N+1) .25 LOCATION of 50th percentile:

– X.50 = (N+1) .50 LOCATION of 75th percentile:

– X.75 = (N+1) .75 Example: If we had 10 scores,

– the 25th percentile would be the (11).25=2.75th score or part way (half way!) between the 2nd and 3rd scores.

– The 50th percentile would be the (11).50=5.5th score, or half way between the 5th and 6th scores.


Example # of pets ever owned

– 13– 2– 1– 4– 0– 1– 3– 0– 5– 1

Put ‘em in order– 0– 0– 1– 1– 1– 2– 3– 4– 5– 13


Note . . . With an odd number of scores, the 50th

percentile will be an actual score: Raw Scores (in order)

– 0– 0– 1– 1– 1– 2– 3– 4– 5– 13– 100

50th percentile = (N+1).50 = (12).5 = 6th score = 2.


Let’s calculate some “averages”


A quiz about averages1 – If one score in a distribution changes, will the mode

change?__Yes __No __Maybe

2 – How about the median?__Yes __No __Maybe

3 – How about the mean?__Yes __No __Maybe

4 – True or false: In a normal distribution (bell curve), the mode, median, and mean are all the same? __True __False


Some rules . . . . . . For building

graphs/tables/charts:– Label axes.– Divide up the axes evenly.– Indicate when there’s a break in the

rhythm!– Keep the “aspect ratio” reasonable.–Histogram, bar chart, line graph, pie

chart, stacked bar chart, which when?– Keep the user in mind.


References Hinton, P. R. Statistics explained. Shaughnessy, Zechmeister, and

Zechmeister. Experimental methods in psychology.

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