Chapter 5 - Key Words Flashcards
Relative standing
How one score compares to the other scores in a sample.
We’ve already talked about relative standing using percentiles. For example a 56th percentile score is one that is greater than 56 percent of the other scores. The median is at the 50th percentile because it is the middle score.
Z-score
A measure of how many standard deviations from the mean a raw score is
Positive z-scores are greater than the mean; negative z-scores are lower than the mean. A z-score of 0.0 is used for scores that are equal to the mean.
Z-distribution
I’m not teaching this to you; you don’t need to understand this term in order to succeed.
Standard normal curve
It’s exactly the same as the curve for the normal distribution.
Sampling distribution of means
I’m going to steal the book’s definition for this one
“A frequency distribution showing all possible sample means that occur when samples of a particular size are drawn from a population.”
This is very similar to the normal distribution of scores, except that the normal distribution of scores is made up of individual raw scores, while the sampling distribution of means is made up of means.
Central limit theorem
This concept is important for mathematics and statistics majors, but not as important for social science majors. Pages 80 and 81 discuss the central limit theorem, but I won’t go over it, and I won’t be testing you on it.
Standard error of the mean
Let’s steal from the book again
“The standard deviation of the sampling distribution of means.”
Z-score calculation
To perform any z-score calculation, you need to have:
A raw score
The sample mean
The sample standard deviation
Z-score calculation (sample)
Raw score: 40
Sample mean: 30
Sample standard deviation: 4
STEP ONE: Raw score – Sample mean; so 40 – 30 = 10
STEP TWO: Divide by the Sample standard deviation; so 10/4 = 2.5
Our z-score is 2.5, which means that our raw score is 2.5 standard deviations above the mean.
The power of algebra
A basic understanding of algebra will give you the ability to find the missing piece in some of the homework and test problems.
For example
Raw score = ? (unknown)
Sample mean = 60
Sample standard deviation = 5
Z-score = 0.6
Let’s solve it!
Finding an unknown raw score
Raw score = ? (unknown)
Sample mean = 60
Sample standard deviation = 5
Z-score = 0.6
Okay, so if the z-score is 0.6, then that means the raw score is 0.6 standard deviations above the mean.
Each standard deviation is 5 raw score points, so 0.6 of 5 is 3 (because 0.6 X 5 = 3).
Now we know that our raw score is 3 points above the mean. The mean is 60, so our raw score is 63.
Finding an unknown sample mean
Raw score = 30
Sample mean = ?
Sample standard deviation = 10
Z-score = 2.0
Our z-score is 2.0, so that means our raw score of 30 is 2.0 standard deviations above the mean.
Each standard deviation is 10 raw score points, 10 X 2.0 = 20, so a raw score of 30 is 20 points above the mean.
30– 20 = 10, so the sample mean is 10.
Using z-scores to find percentiles
Page 253 of the book features the z-table. If you have your book with you go ahead and open it up. If not, then wait until you have your book with you before you go through the next few slides to do the homework.
Look at the last slide. Did you notice how each standard deviation marked a certain percent (or proportion) of scores? The gap between the mean (z-score of 0.0) and the first positive standard deviation (z-score of 1.0) includes 34.13 percent (or a proportion of .3413) of all the data in a normal distribution of scores.
So if you have a z-score of 1.0, then your percentile score is about 84th percentile. Because it’s higher than all the negative z-scores (which are 50% of the distribution) and all the positive z-scores that are less than 1.0 (which are about 34% of the distribution), and 50 + 34 = 84.
Using z-scores to find percentiles
What if your z-score was -0.71? How could you calculate your percentile?
Turn to page 253.
Find the z-score of 0.71 near the bottom of the second column of z-scores (4th column overall).
It says the area between the mean and this z-score is .2611; in other words 26.11 percent of the distribution is between the mean and the z-score of 0.71.
We know that 50 percent of the distribution’s scores are above the mean, and 26.11 percent of the distribution’s scores are between your z-score of -0.71 and the mean.
50 + 26.11 = 76.11, so 76.11 percent of the distribution’s scores are higher than yours.
100 – 76.11 = 23.89, so your score is at the 23.89th percentile.
USING z-scores to find percentiles
What if your z-score was -0.71? How could you calculate your percentile?
Turn to page 253.
Find the z-score of 0.71 near the bottom of the second column of z-scores (4th column overall).
It says the area between the mean and this z-score is .2611; in other words 26.11 percent of the distribution is between the mean and the z-score of 0.71.
We know that 50 percent of the distribution’s scores are above the mean, and 26.11 percent of the distribution’s scores are between your z-score of -0.71 and the mean.
50 + 26.11 = 76.11, so 76.11 percent of the distribution’s scores are higher than yours.
100 – 76.11 = 23.89, so your score is at the 23.89th percentile.
