# Variability - PowerPoint PPT Presentation

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Variability. Chapter 4. What is it?. How much difference there is from person to person How spread out scores are No variability = all scores are the same. Why do we care?. Less variability = more know about the population based on the sample

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Variability

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## Variability

Chapter 4

### What is it?

• How much difference there is from person to person

• How spread out scores are

• No variability = all scores are the same

### Why do we care?

• Less variability = more know about the population based on the sample

• Less variability = more any one person can tell you about the group that he or she is from

### To keep in mind

• Two groups of scores can have the same mean, but different amounts of variability

• Two groups of scores can have different means, but the same amount of variability

•  mean and variability measure two different things

### Quantifying variability

• Range = number of scores between the highest and lowest scores

• Problem = only the highest and lowest scores matter

• Outlier high range

• Can use interquartile range instead, which just addresses number of scores between highest and lowest, once top and bottom 25% have been lopped off

• Still not as good of a measure as we’d like to use

### Standard Deviation

• Ideal measure of variability

• Tells about average distance of scores from mean

• i.e., how much do scores deviate from the mean of the group

• Keep in mind: standard deviation tells about all the scores

### Calculating standard deviation

• Most straightforward:

• Take each score, subtract the mean

• Take the mean of those difference scores

• Problem: always get zero

### To avoid zero

• First calculate variance (average squared distance of each score from the mean)

• 1. take each score, subtract the mean

• 2. square that difference

• 3. add up across all scores

•  sum of squares (sum of the squared difference between each score and the mean, SS)

• 4. divide

### Divide by what?

• Depends on who you have information from

• If you have information from all the people you care about, divide by the total number of scores you have (n)

•  s2 = variance

• If you have information from a sample, but want to estimate variability for the population, divide by one less than the total number of scores you have (n-1)

• n-1 = df = degrees of freedom

•  s2 or SD2 = variance

• To get from variance to standard deviation, want to get from average squared distance between each score and the mean to the average distance between each score and the mean

•  regardless of whether using formula for population or for sample, take the square root

•  s or s (or SD)

### What is s, or SD, exactly?

• Estimate of how much variability there is in the population, based on how much variability there is in the sample

• Will not be exactly the same, but will give a good estimate

### Be sure to keep in mind

• What, in English, are:

• Sum of squares

• Variance

• Standard deviation

• How to calculate, for population, and to estimate in a population based on the sample

• Symbols

• What it all means