Explain the different columns in a computational table.
- The first column is always the raw score.
- Every other column is custom designed for the equation you’re solving for. The computations you’re making dictate the columns you use Only one computation per column.
- Every computation table has a summation row.
Why are computation tables useful?
- They are a clean and effective way of showing you’re work.
What are two things not to do in a computation table?
- No busy work between columns
- Fitting in equations.
What are the two parts of a deviation score?
1) Sign - tells us whether a raw score is below (-) or above (+) the mean.
2) The number - tells us the actual distance from the mean in units measured.
How do you calculate the mean deviation score?
Take the sum of the deviation scores divided by the number of deviation scores (N)
What will the mean deviation score always equal? Why?
The numerator will always add up to zero, thus the equation will always equal zero. This is because the sum of all of the deviation scores will add up to zero, as some will fall above and below 0.
The mean of the deviation scores will always equal zero.
Therefore the mean of the deviation scores has no value as a measure of variability.
Explain the first solution to avoid the problem of the mean deviation score equaling zero.
- Ignore the signs and use the absolute values of the deviation scores
- Called the average deviation = mean of absolute values of deviation scores
But, turns out that the average deviation for a sample does not represent the population it comes from.
i.e. can’t use it as an inferential statistic.
Explain the second solution to avoid the problem of the mean score equaling zero.
- Mathematically get rid of these signs by squaring each of the deviation scores.
Leads us to Variance = the average of the square deviation scores.
What is the definitional formula of variance?
Σ(X - μ)²/N
AKA
SS/N
How do we avoid rounding error when calculating variance?
Use the computational formula for variance.
What is the computational formula for variance?
(Σx² - (Σx)²/N)/N
This is the mathematical equivalent of Σ(X - μ)²/N
What are two reasons that variance is great?
- It is stable: it doesn’t change much across the sample
- The more variable the data, the greater the variance and vice versa. AKA: it’s accurate.
What is one problem with variance?
It is in squared units. Therefore there is some disconnect with the data.
If DV is how many egg McMuffins a person eats, have you ever seen a squared egg McMuffin?
Give the definition for standard deviation.
The standard deviation is the standard, or typical difference a raw sore is from its mean.
It is NOT the mathematical average, t is the standard, or typical difference. It’s better than average.
How do we get a measure of variability in original measurement units?
Take the square root of variance –> that gives us the equation for standard deviation.
σ² = population variance
σ = population standard deviation
σ = √σ²
What are two great qualities about Standard Deviation?
- It is in original measurement units
- It is stable
What would happen if we calculated the variance of a sample using the equation Σ(X - μ)²/n?
It would be biased (AKA wrong)
This is because samples tend to be less variable than their populations..
How do we correct the bias of calculating the variance of a sample using the equation Σ(X - μ)²/n?
Divide the SS by its degrees of freedom.
SS/df = Σ(X - μ)²/n-1
Which of S² and S is biased? Which is unbiased?
S² (sample variance) is unbiased but S is biased.
Why can’t both S² and S be unbiased?
They are related by a square root relationship, square root relationships are non-linear. Therefore both can not be unbiased.
There is a curve in the linear relationship, i.e. not a one to one relationship between S² and S.
Why do we analyze variance and not standard deviation?
Because variance is unbiased, and standard deviation is biased.
What do we use S² for, and what do we use S for? Why?
We use S² as an inferential statistic because it is unbiased. But it is in squared units. Therefore we use S as a descriptive statistic.
