What does more variance indicate?
A stronger correlation.
What is variance?
Variance represents the amount of variability in the data.
- 3 main methods of representing variability.
1) range -simplest one
2) Standard deviation (S)
3) Variance (S2)
What is correlation?
- Standardised representation of the association between 2 variables.
- Can range from-1.0 to 1.0
- r symbol for correlation
How to calculate variance
- square standard deviation
- square the correlation (coefficient determination)
What are composite variables?
- Test scores based on the sum of 2 or more items.
- E.g. The Beck Depression Inventory consists of 21 items
- Items are scored on an ordinal scale from 0 to 3
- Thus, the range of scores possible on the BDI is 0 to 63. (3x21)
- Such ‘sum scores’ are known as ‘composite scores’.
The variance of a composite score is a function of:
- The variance associated with the individual items, and
2. The correlation amongst the items.
As the correlation between items increases (and is positive) what also increases?
The magnitude of the corresponding composite variance score.
Binary items (dichotomous items)
- you either provide the correct or incorrect answer.
- Responses are scored 0 or 1.
- Frequently used in achievement type tests
- E.g. Exams and intelligence test items
Binary items: variance
-The variance of a dichotomously scored item is maximised when half of the people score 1 and the other half score 0.
What are the most common psychological test score interpretations?
1) Relative interpretations - based on the analysis if data
2) Abstract interpretations - based on the research which supports the test scores as valid indicators of a psychological construct.
Relative interpretations - to interpret an individual’s score, we need to:
-know the mean and SD
Raw Scores: Limitations
- Although the mean and SD allow us to interpret a particular score in a relative way, it is not a precise method, unless you’re a human calculator.
- Instead, raw scores can be converted into standardised scores which incorporates information about the mean and SD.
- The most commonly used standardised score is the z-score.
Z-scores
- Have a mean of 0 and SD or 1.
- Useful for transforming raw scores into relative scores.
- Shows us the distance from the mean and so frees us from worrying about the units of the original test score.
- Can be used to compare scores across tests that are on different sized units.
- Even if the scales are meaningful, you may want to convert them for the purposes of comparison.
Converted Standard Scores
- Z-scores are great but if you didn’t want to deal with negative numbers you can convert them into alternative standard scores.
- To do this rescale the scores so that the converted scores have a different mean and SD.
- The most popular is the T-score
- With T-scores the mean is always 50 and the SD is always 10.
- T-scores are not like t-tests; they’re different.
How to create T-scores
1) convert the raw scores unto Z-scores
2) Then, convert the z-scores using the formula: T = z(10) + 50
Is this dodgy?
- You may think that applying these conversions is dodgy.
- However you have to remember that most psychological tests yield scores that have no inherent meaning.
- They are measured on ordinal scales.
- They simply yield information in a relative sense.
- How we scale those raw scores does not alter their inherent relative meaning.
- In the case of academic marks, there is one aspect to consider.
- They’re considered “criterion referenced” in a sense.
- That is you need to achieve 50 to pass.
What are percentile ranks?
- Percentile ranks indicate the percentage of scores that are below a specific test score.
- another way to represent scores in relative terms.
What is a reference sample the same as?
Normative samples.
Probability and Non-Probability Sampling
- Probability samples use procedures that ensure a representative sample.
- Random sampling is a type of probability sample, as you would expect a random sample from the population to be representative of the population.
