Bedrock Statistics in Psychological Measurement Part 1

Variance, SD, Z-score + Basics in Jamovi

Four levels of measurement

Nominal

Ordinal

Interval

Ratio

Nominal

Categories and labels variables

Ordinal

Categories and labels variables

ranks categories in order

Interval

Categories and labels variables

ranks categories in order

has known, equal intervals

Ratio

Categories and labels variables

ranks categories in order

has known, equal intervals

has a true or meaningful zero

Variance

index of the extent to which scores in a distribution deviate from their central tendency (i.e., mean)

average squared deviation from the mean

Deviation

Difference between each score and the mean

Problem with deviations

if we average the deviations, they add up to 0 because positive and negative deviations cancel each other out

Solution to problem with deviations

square each deviation before averaging them, so they don’t cancel out → gives us variance

What can the standard deviation tell us

understand how far a persons score is from the average

how spread out scores are from the mean in original units (e.g., exam points)

Why is using standard deviation helpful

tells us how unusual a score is relative to the rest of the distribution

a score that is far from the mean in terms of SDs is more deviant than one close to the mean

Z-score

tells us how many standard deviations a score is above or below the mean

one specific score is from the mean, measured in standard deviations

How we interpret z-score

0: score is exactly at the mean

+1: score is 1 SD above the mean

-1: Score is 1 SD below the mean

+2: Score is 2 SD above the mean

Why are z-scores useful

z-scores let us compare scores from different distributions, even when they have different means and SD

How do we know who scores better when looking at z-scores (exams)

Higher the z-score the better

**have to use mean and SD and score to convert to Z score

Standard normal z-distribution

shows how scores are distributed around the mean after being converted to z-scores

Percentile

percentage of people who scored below a particular score

if you’re at the 90th percentile, you scored higher than approximately 90% of people in the distribution

tells you where you stand relative to others

How can a higher percentile be good

usually good because it means you scored higher than more people

How can a higher percentile be bad

if it means you have more symptoms or higher levels of a problem than most people