Download EDUC5504 Chapter Eight

Chapter Eight
Closed Book Information:
1. The study of ______ probability is the basis for the normal curve and the foundation of
inferential statistics. The normal curve provides us with a basis for understanding the
_________ probability (same word as first blank) associated with any possible outcome.
2. The tools of probability and the study of the normal curve allow a researcher to
determine the mathematical likelihood that a difference found between two research
outcomes is not due to ___________ chance.
3. Be able to identify the three characteristics that are associated with the normal curve
a. Mean, median and mode are the same.
b. Perfectly symmetrical about the mean
c. Asymptotic-tails of the curve come closer and closer to the X axis but never touch
4. Be able to identify the relative probability of events that occur at various standard
deviations of the normal curve.
a. 0+1 or -1 = 34% (50-34 and 50+34)
b. (+1 or – 1) + 2 or -2 = approx. 14%
c. (+2 or -2) to 3 = approx. 2%
d. At negative one standard deviation, what % of cases are included? 16%
e. Positive 1? 84%
f. Positive 2? 98%
g. Negative two? 2%
5. In a normal distribution almost 100% of all scores occur between ___negative three____
standard deviations and __positive three______ standard deviations.
6. Standard scores (such as z scores) allow researchers to do something that they cannot
do with raw scores? What is that?
a. Compare distributions; that is compare scores that are on different scales and have
different means and standard deviations
7. Standard scores are comparable because they are standardized in units of _____ _______
standard deviations.
8. Z scores that are below the mean are ____negative_____ and z scores that are above the
mean are ___positive________.
9. Positive z scores always fall to the __right_____ of the mean and are in the _upper_____
__half_____ of the distribution. Negative z scores always fall to the __left_____ of the mean
and are in the __lower____ __half______ of the distribution.
10. A z score is simply the number of __standard______ __deviations______ from the mean.
11. When raw scores are represented as standard scores such as z scores, they are
__comparable________.
12. In hypothesis testing, if an event (score, outcome) seems to occur only ___5___ times (or
less) out of 100, (__5___%), we will deem that event to be rather unlikely relative to all
other events that could occur.
13. Applying the concept in #12 to research, we know that if you are comparing two
outcomes in a research study (e.g., traditional approach to teaching reading vs. new
method to teaching reading) and the new reading approach yields a higher score than
the traditional approach at a probability level of .05 or less, we can assume that the
higher scores are not due to __chance________. This means that there is only a 5 out of 100
(or 1 out of 20) possibility that the event that is occurring is a result of mere chance; so we
believe that it indicates there is a real difference between the teaching methods.
Remember that for every mean true score (mean of all the true scores of the subjects
being measured) there is error. This error around the true score creates a range
within which the observed score might fall—possibly above; possibly below. So, when
we begin to compare the scores of two different groups, we have to realize that in
order to be sure that one is actually superior to the other, you have the scores falling
fall enough apart that the ranges of the true scores of each group are barely
overlapping. So we want the probability of this chance for overlap to be no greater
than a 5% chance.
Open Book Information:
1. Given a picture of the normal curve, be able to
a. Write in a rounded percentage figure for each area of the distribution between
standard deviations
b. Identify where the mean is located
c. Identify the approximate percentile rank for each standard deviation
2. Given a set of raw scores, be able to convert the scores to z scores.
Z = _(X –X-bar)___
s
3. Using Table B.1 in the appendix of your text and raw scores that you have converted to z
scores, be able to determine the probability of a score falling
a. above or below a particular score.
What is the probability of a score falling between above a z-score of 2?
Z = 47.72/add this to 50% (mean)/ get 97.72 and round to 98%/ 2% odds of falling
above a z-score of 2
What is the probability of a score falling below a z-score of -1.5?
Z = 43.32/ subtract from 50 to get 6.68 or about 7th percentile—about 7%
b. between two particular scores
What is the probability of a score falling between a z-score of -1.5 and 2?
Draw a picture!!!
About 43% to 50 + about 48% from 50 to 98/ add together/ about 91% chance of a
score falling between -1.5 and +2.0