HIM 505 Chapter 3
The formulas used to compute them are very similar. You see them all over the place in the __ sections of journals.
"Results"
Then, it divides the sum by the size of the __ (minus 1) and takes the ____ of the result.
- sample -square root
___ them and __ by the number of data points, and you have the mean deviation.
-Sum -divide
the standard deviation (abbreviated as s or SD) represents the ___ amount of ____ in a set of scores.
-average -variability
The moral of the story? When you compute the standard deviation for a sample, which is an estimate of the population, the ___ to the size of the population the sample is, the more ___ the estimate will be.
-closer -accurate
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MUST READ NOW
Here are the data we'll use in the following step-by-step explanation of how to compute the standard deviation: 4. __ each individual difference.
Square
___ is each individual score.
X
___ is the mean of all the scores.
X (X bar)
Instead, let's take the ___ value of each deviation (which is the value regardless of the sign).
absolute
The larger the standard deviation, the larger the average distance each ____ is from the mean of the distribution.
data point
Actually, how ____ differ from one another is a central part of understanding and using basic statistics.
data points
Here are the data we'll use in the following step-by-step explanation of how to compute the standard deviation: 1. List ____. It doesn't matter whether the scores are in any particular order.
each score
There really are two kinds of ranges. One is the _____, which is the highest score minus the lowest score (or h - l) and the one we just defined.
exclusive range
The range is used almost exclusively to get a very ___ estimate of how wide or different scores are from one another—that is, the range shows how much spread there is from the lowest to the highest point in a distribution.
general
____ is the highest score in the data set.
h
r = ____
h - l
You are not likely to see the variance mentioned by itself in a journal article or see it used as a descriptive statistic. This is because the variance is a difficult number to ___ and apply to a set of data.
interpret
In other words, s2 = s × s, or the variance equals the standard deviation times __ (or squared).
itself
___ is the lowest score in the data set.
l
If you take the standard deviation and never complete the ____, you have the variance.
last step (taking the square root)
And what "score" do you think that might be? Well, instead of comparing each score to every other score in a distribution, the one score that could be used as a comparison is—that's right—the ___.
mean
Here are the data we'll use in the following step-by-step explanation of how to compute the standard deviation: 2. Compute the ____ of the group.
mean
In practical terms, it's the average distance from the ____.
mean
So, variability becomes a measure of how much each score in a group of scores differs from the ___.
mean
The average deviation for all scores from the mean of a distribution, calculated as the sum of the absolute value of the scores' deviations from the mean divided by the number of scores.
mean deviation
___ is the sample size.
n
They are also quite different. First, and most important, the standard deviation (because we take the square root of the average summed squared deviation) is stated in the ___ from which it was derived.
original units
First, here's the formula for computing the standard deviation:
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variance formula
page 49
___ is the range.
r
___ is the standard deviation.
s
If you know the standard deviation of a set of scores and you can square a number, you can easily compute the variance of that __ set of scores.
same
Dividing by a ____ lets us do so. Thus, instead of dividing by 10, we divide by 9. Or instead of dividing by 100, we divide by 99.
smaller denominator
Variability (also called __ or ___) can be thought of as a measure of how different scores are from one another.
spread or dispersion
A conservative estimate of a population parameter.
unbiased estimate
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example and SPSS
This formula finds the ___ between each individual score and the ___ (X - X), ___ each difference, and ___ them all together.
-difference -mean -squares -sums
It's even more accurate (and maybe even easier) to think of variability as how ___ scores are from _____ score.
-different -one particular
Sometimes it's called ___,____ or ___, or one of many other terms, but the fact is, variety is the spice of life, and what makes people different from one another also makes understanding them and their behavior all the more challenging (and interesting).
-fluctuation, or -lability, or -error
But we're more interested in __ these __ are used, so let's take a look at one such study that actually focused on variability as an outcome.
-how - tools
The range is computed simply by subtracting the __ score in a distribution from the ___ score in the distribution.
-lowest -highest
Three measures of variability are commonly used to reflect the degree of variability, spread, or dispersion in a group of scores. These are the ___,___ and the ____.
-range, -standard deviation, -variance
Now we get to the most frequently used measure of variability, the _____. Just think about what the term implies—it's a deviation from something (guess what?) that is standard.
standard deviation
The average amount of variability in a set of scores or the scores' average deviation from the mean.
standard deviation
This third measure of variability, the variance, is sim- ply the __________.
standard deviation squared
Why do we divide by n - 1 rather than just plain ol' n? The answer is that s (the standard deviation) is an estimate of the population standard deviation, and it is an ____ at that, but only when we subtract 1 from n.
unbiased estimate
How much scores differ from one another or, put another way, the amount of spread or dispersion in a set of scores.
variability
In the most simple of terms, ____ reflects how scores differ from one another.
variability
How are standard deviation and the variance the same, and how are they different?Well, they are both measures of ___,___ or ___.
variability, dispersion, or spread
The square of the standard deviation and another measure of a distribution's spread or dispersion
variance
You already know that the sum of the deviations from the mean must equal ___ (otherwise, the mean is computed incorrectly).
zero
____ is sigma, which tells you to find the sum of what follows.
Σ
So, although the range is fine as a general indicator of variability, it should not be used to reach ____ regarding how individual scores differ from one another.
any conclusions
But the variance is important because it is used both as a ___ and as a practical measure of variability in many statistical ___ and ___.
-concept -formulas and techniques
Here are the data we'll use in the following step-by-step explanation of how to compute the standard deviation: 3. ____ the mean from each score.
Subtract
Here are the data we'll use in the following step-by-step explanation of how to compute the standard deviation: 5. ___ all the squared deviations about the mean.
Sum
That's what mainline statisticians spend lots of their time doing—looking at the ___ and ___ and ___ (and the violation thereof) of certain statistics.
characteristics and performance and assumptions
Biased estimates are appropriate if your intent is only to describe the ___ of the ___.
characteristics of the sample
The standard deviation is computed as the ___ from the mean. So, you will need to first compute the mean as a measure of central tendency. Don't fool around with the median or the mode in trying to compute the standard deviation.
average distance
Why would we want to do that? Because, as good scientists, we are ___. Being _____ means that if we have to err (and there is always a pretty good chance that we will), we will do so on the side of overestimating what the standard deviation of the population is.
conservative
By subtracting 1 from the ___, we artificially force the standard deviation to be larger than it would be otherwise.
denominator
Now, add your new knowledge about variability—that it reflects how different scores are from one another. Each is an important ______.
descriptive statistic
Just to whet your appetite, consider this: The standard deviation can be used to help us compare scores from _____, even when the means and standard deviations are different. Amazing!
different distributions
Together, these two (average and variability) can be used to describe the characteristics of a ___ and show how ___ differ from one another.
distribution
So, if you have a set of scores such as 3, 4, 5, 5, 8 and the arithmetic mean is 5, the mean deviation is the sum of 2 (the absolute value of 5 - 3), 1, 0, 0, and 3, for a total of 6. (Note: The absolute value of a number is usually represented as that number with a vertical line on each side of it, such as |5|. For example, the absolute value of -6, or |-6|, is 6.)
example
Just like the mean, the standard deviation is sensitive to ____. When you are computing the standard deviation of a sample and you have ___, note that fact somewhere in your written report.
extreme scores
The second kind of range is the ____, which is the highest score minus the lowest score plus 1 (or h - l + 1).
inclusive range
But when it comes to differences between ____ and ___ (a mainstay of most social and behavioral sciences), the whole concept of variability becomes really important.
individuals and groups
The _____ (also called the mean absolute deviation) is the sum of the absolute value of the deviations from the mean divided by the number of scores.
mean deviation
Here are the data we'll use in the following step-by-step explanation of how to compute the standard deviation: 6. Divide the sum by ____
n - 1
If s = 0, there is absolutely ___ in the set of scores, and the scores are essentially identical in value. This will rarely happen.
no variability
But if you intend to use the sample as an estimate of a _____, then it's best to calculate the unbiased statistic.
population parameter
The ____ is the most general measure of variability. It gives you an idea of how far apart scores are from one another
range
The positive difference between the high- est and lowest score in a distribution. It is a gross measure of variability. Exclusive __ is the highest score minus the lowest score. Inclusive __ is the highest score minus the lowest score plus 1.
range
This is exactly what Nicholas Stapelberg and his colleagues in Australia did when they looked at variability in heart rate as it related to coronary heart disease. Now, they did not look at this phenomenon directly, but they entered the search terms "heart rate variability," "depression," and "heart disease" into multiple electronic multiple databases and found that decreased heart rate variability is found in both major depressive disorders and in coronary heart disease. Why might this be the case? The researchers think that both diseases disrupt control feedback loops that help the heart function efficiently. This is a terrific example of how looking at variability can be the focal point of a study, rather than an accompanying descriptive statistic.
real-world statistic example
You most commonly see the exclusive range in research articles, but the inclusive range is also used on occasion if the ____ prefers it.
researcher
Remember what you already know about computing averages—that an average (whether it is the mean, the median, or the mode) is a representative score in a __ of ___.
set of scores
The larger the standard deviation, the more _____ the values are, and the more different they are from one another.
spread out
Here are the data we'll use in the following step-by-step explanation of how to compute the standard deviation: 7. Compute the ____
square root
In other words, it's the same formula you saw earlier but without the ____
square root bracket
The variance is stated in units that are ___ (the square root of the final value is never taken).
squared
As you can see, and as we mentioned earlier, the ____ is an average deviation from the mean.
standard deviation