Winslow Homer: “On The Stile” 1878

INFERENTIAL INFERENTIAL PROBLEM SOLVINGPROBLEM SOLVING

Hypothesis Testing and t-tests

Chapter 6:133-149

QUESTION:QUESTION:

Suppose you have a REALLY GOOD QUESTION...

And you want a And you want a “scientific” answer…“scientific” answer…

Let’s say you would like to know if gender influences height (Are men taller than women?)...

What steps might you take to solve this problem?

Step 1:Step 1: State your Hypothesis:

Turn your question (Are men taller than women?)

Into A Null Hypothesis: Null “guess” (Men are no taller than women)

STEP 2: Get representative STEP 2: Get representative samples:samples:

Next Steps:Next Steps:1. Measure the heights of a group

of men and a group of women…2. Calculate the means of each

group3. Compare the means of the two

groups…4. VOILA! Make your conclusion!

But what if the women were basketball players, and the men were gymnasts?

Horrors! Horrors! You publish a conclusion that is false!Avoiding this tragic situation:

1. Avoid “TYPE I Errors:You conclude MEN ARE taller, when

in fact they are not2. Avoid “TYPE II Errors:

You conclude MEN ARE NOT taller, when in fact they are

1. Reducing the Risk: Sampling 2. Accepting some Risk: p = Probability

A Word About Sampling…A Word About Sampling… Researchers want to know the characteristics of a

large group or “Population” (i.e. all women vs all men). IMPOSSIBLE!!

However a representative “sample” can be selected

Results are then inferred to also apply to the population.

Samples are randomly selected Must be large enough to detect differences and

minimize the impact of “outliers”

How Big of a Sample?How Big of a Sample?Depends:

Type of Question (experimental, descriptive, correlational, survey…)

Degree of Accuracy requiredNormal variability observed

In General: For “quasi-experimental” (like this)

you need about 30

PED 471: Height HistogramPED 471: Height HistogramSpring 2001Spring 2001

One More Time: Compare Mean Heights and Standard Deviations:

Does the male group overlapThe female group? If so, how much?

What are the Statistics What are the Statistics Used?Used?We can compare means of two

groups: Groups can be “Independent”

(Cross-sectional – men vs women)

Or “Dependent” (Longitudinal: Pre-Post)

The Paired t-test:The Paired t-test: Analyzes whether or not the difference

in means between the two groups are in fact Statistically Significant

Evaluates the “overlap” of the variability of each mean

Determines the PROBABILITY that by rejecting the Null Hypothesis, you would be WRONG

Written as p < .05

One Last Detail: One Last Detail: TAILS: TAILS: The ends of the normal

distribution: One-tailed t-Test: One-tailed t-Test:

Men will be taller (the tall end of the normal distribution)

Two-tailed t-Test:Two-tailed t-Test:Men will be different (could be

taller or could be shorter…either end of the distribution)

Finally: Using the t-Test, Finally: Using the t-Test, determine the probability determine the probability (p) of making a false (p) of making a false conclusion:conclusion: P<0.05 means that there is less

than a 5% chance that the measured difference is not a true representation of the populations (TYPE I Error)

Let’s try itLet’s try it... Use your height and shoe size database1. State the Null Hypothesis about heights

and shoe sizes between genders2. Determine the samples (dependent or

independent-paired)3. Determine the acceptable probablility

of making a Type I Error (p < .05)4. Determine whether your hypothesis is

one or two tailed…

And Run It!And Run It!Analyze the Means of the Men’s

and Women’s heights and shoe sizes with the TTEST in EXCEL

\\Nss-data\vol1\teachers\BaEngeb1\my_docs\PED471\ht.ss.data.xls

SUMMARY:SUMMARY:State the Null Hypothesis: A

“neutral” guess about the expected group differences

Select Representative Sample from which we will infer a conclusion about the Population

Determine the acceptable probability of making a Type I Error in your conclusion

Summary ContinuedSummary Continued: When your question involves comparing

two means, determine: Independent Groups OR Dependent (pre-post test) Groups

Determine the hypothetical “Tails” (1 or 2)

Use the t-Test to calculate Statistical Significance: The acceptable probability of making a Type I Error in your conclusion is less than P < 0.05 (Less than 5%)

Hoop Shoot Lab:Hoop Shoot Lab:We will do an experiment to help us

answer this question: Does 5 minutes warm-up improve free

throw accuracy?Write your null hypothesis, samples,

probability of Type I Error, and number of tails

Design an experiment using this class as your “sample”…