Ch 3: Differences, Consistency, Test Scores Flashcards
Variance - Definition
- Statistical way of quantifying variability/individual differences in a distribution
- Tells you how far each data point is from the mean & every other data point
Interindividual Variability - Definition
Differences that exist between people
Intraindividual Variability - Definition
Differences that emerge in one person over time or under different circumstances
What factors determine the size of the variance?
1) How much the scores in a distribution differ from each other (duh)
2) Metric of the scores in the distribution
Variance - Formula
N - sum of squares / nr of scores
Variance (Binary) - Formula
p(1-p)
- p = proportion of Yes answers
Can the variance/SD be 0?
No, because this would mean that there are no differences in the data points at all, meaning that everyone would essentially have the same score
Covariance - Definition
Degree of association between the variability in the two distributions of scores
Covariance - Formula
N - sum of the cross product of deviation scores X & Y divided by the total number of observations
What information can be discerned from the covariance?
The direction of the association (not the magnitude though)
Correlation - Definition
Index of linear association between two variable, expressed as a value between -1 and +1
Correlation - Formula
(SDx)(SDy)
What information can be discerned from the correlation?
- direction of association
- magnitude of association
Central Tendency - Definition
The score that is the most representative of the entire distribution
What is the most commonly used reflection of central tendency?
The mean
What is the distribution of data when there is a positive skew?
- There are few data points above the mean
- Distribution is skewed to the left (most values are below the mean)
What is the distribution of data when there is a negative skew?
- There are few data points below the mean
- Distribution is skewed to the right (most values are above the mean)
Skew - Formula
(N)(SD³)
Raw Score - Definition
Scores obtained most directly from the responses to test items
Percentile Rank - Definition
Percentage of scores that are below a specific test score
How do you calculate the percentile rank using raw scores?
(nr of ppl w lower score÷total nr of scores)x100
How do you calculate the percentile rank using z scores?
Note: use a normal distribution table for this
if Z score is positive:
(Area) + 0.5 x 100
if Z score is negative:
0.5 - (Area) x 100
Z score - Definition
Number of standard deviations by which the raw score is above or below the mean
Z score - Formula
SD
Z score - Statistical Properties
- mean = 0
- SD = 1
What are the benefits of using z scores?
- it is not ambigious
- it allows for the comparison of scores that have differing unit scales
- expresses score in relative terms
What are the limitations of z scores?
Z scores are not intuitively understandable for many people
Standardised Scores - Definition
- Z scores that have been converted into values that people find easier to understand.
- scores are rescaled to have a different mean and SD
Standardised Scores - Formula
Ti = (ZSCORE)(SDnew) + (MEANnew)
When do you conduct a normalisation transformation?
When the data is not normally distributed
What are the assumptions underlying a normalisation transformation?
1) The construct being measured is actually normally distributed
2) The collected data is an imperfect reflection of the actual (normal) distribution
Normalisation Transformation - Steps
1) Convert Raw Scores into Percentile Ranks
(nr of ppl below/total) x 100
2) Convert Percentile Ranks into Z Scores
(p.rank/100) - 0.50
3) Convert Z score into Standard Score
(zscore)(newSD) + (newMean)
Test Norms - Definition
The scores of a large group of people is used as the reference sample
