Psychometrics Exam Summary
Week 1: Measuring, Scaling & Norms
Psychological Testing
Systematic Behavioural Sample = use it to reflect a person’s general behaviour
BDI = asks how often someone has displayed a particular behaviour in the past week
Inter-Individual Differences = differences between people
Intra-Individual Differences = differences within one person
Measurement Errors
Psychometrics = aims to evaluate the properties of a test in a systematic way
Random Errors = e.g. our behavioural sample includes that week that you happen to be ill
Systematic Errors = e.g. when we administer the test, question does not measure what we want
Psychometric Properties:
Reliability =
absence or presence of random errors
Validity = existence of systematic errors
Scaling
Nominal = most basic level of measurement. To measure nominally, the variable has to be:
1. Exhaustive = you have included every possible option
2. Mutually Exclusive = it is impossible to be in two categories at once
Ordinal = labels which can be organised in some type of order (no specific numbers, just an order)
Interval =
the numeric labels have more meaning because the distance between these labels is the
exact s ame everywhere (difference b/w 1cm-2cm is the same as 3cm-4cm)
We do not have an absolute zero, we have an A
rbitrary Zero = having the label ‘0’ does not mean
that there is absence of the trait or behaviour - the label ‘0’ is a reference point
● Good example → IQ level
Ratio = the numeric labels have their “full” meaning: the distances between labels are all the same
and we have an Absolute Zero = the ‘0’ labels for total absence of the construct
● Good example → length & weight
Scale Scores = scores we compute by adding all item-scores together or taking the mean of them
,Norms
2 ways of interpreting tests:
1. Criterion Referenced Testing = there is a specific criterion that needs to be met in order to
‘pass’ or ‘succeed’ in a particular testing situation
Involves A
bsolute Norms = norms needed to be set beforehand, independent of the test results
2. Norm Referenced Testing = designed to compare and rank testtakers in relation to one another
Involves R
elative Norms = norms obtained from other people taking the same test
Norm Scores:
Z-Score =
shows the number of standard deviations any given score is from the mean
The mean has a standard score of 0 and a score that is one std. dev. from the mean is 1
Z-scores can also be negative, indicating std. devs. below the mean
Formula → Z x = X −X
Sx
- X = individual score of a person on the test
- X = mean score on the test
- Sx = standard deviation of the test
T-Score = a rewritten z-score → we convert z-scores into t-scores to gain a more intuitive set of
scores for a variable that we can communicate easily to people that do not know means or std. devs.
The mean score is set at 50 and the std. dev. is set at 10
Formula → T x = 10 * X Sx
−X
or
T x = 10 * Zx + 50
Percentile Score =
the % of people that obtained the same/lower score than any particular score
Cumulative Percentage= add the % of people with same score to the % of people with lower score
- High Percentile Score → indicates a high score
- Low Percentile Score → indicates a low score
COTAN = the organisation that routinely checks psychological tests in the Netherlands
You do not want to base your norms on a too small group and definitely not on a group from a few
decades ago, as these norms will likely not be representative of the population
, Week 2: Reliability
Classical Test Theory
Classical Test Theory (CTT) = a theory based on the idea that every observed score (Xo) consists
of a true score (Xt) and the measurement error of the instrument (Xe)
True Score = always a l atent score, we cannot directly observe it
Error = indicates difference between the true score and observed score
- Negative Error = when the true score is higher than the observed score
- Positive Error = when the true score is lower than the observed score
Formula → X o = Xt + Xe
Three specific assumptions in CCT:
1. μ e = 0 → the mean of the errors in the population is equal to 0
2. ret = 0 → the errors do not correlate with the true scores
3. reiej = 0 → the errors are independent and do not correlate with each other
a. All these assumptions ay that the errors have to be random, not systematic
The observed variance can be split in part true variance and part error variance. The rest is that the
observed variance (So2) is equal to the true variance of the scores (St2) and the variance of the error
(Se2) added together (= basically the same as before)
Formula → So2 = St2 + Se2
Reliability Coefficients
Reliability Coefficient = Rxx
St 2
Formula → Rxx = So 2
- St2 = true variance
- So2 = observed variance
The observed variance exists out of true variance and error variance. The more true variance there
is, therefore the less error variance there is, the more reliable our test is
- Reliability of 0.70 is good enough for research
- Reliability of 0.80 is good enough for individual diagnosis
Week 1: Measuring, Scaling & Norms
Psychological Testing
Systematic Behavioural Sample = use it to reflect a person’s general behaviour
BDI = asks how often someone has displayed a particular behaviour in the past week
Inter-Individual Differences = differences between people
Intra-Individual Differences = differences within one person
Measurement Errors
Psychometrics = aims to evaluate the properties of a test in a systematic way
Random Errors = e.g. our behavioural sample includes that week that you happen to be ill
Systematic Errors = e.g. when we administer the test, question does not measure what we want
Psychometric Properties:
Reliability =
absence or presence of random errors
Validity = existence of systematic errors
Scaling
Nominal = most basic level of measurement. To measure nominally, the variable has to be:
1. Exhaustive = you have included every possible option
2. Mutually Exclusive = it is impossible to be in two categories at once
Ordinal = labels which can be organised in some type of order (no specific numbers, just an order)
Interval =
the numeric labels have more meaning because the distance between these labels is the
exact s ame everywhere (difference b/w 1cm-2cm is the same as 3cm-4cm)
We do not have an absolute zero, we have an A
rbitrary Zero = having the label ‘0’ does not mean
that there is absence of the trait or behaviour - the label ‘0’ is a reference point
● Good example → IQ level
Ratio = the numeric labels have their “full” meaning: the distances between labels are all the same
and we have an Absolute Zero = the ‘0’ labels for total absence of the construct
● Good example → length & weight
Scale Scores = scores we compute by adding all item-scores together or taking the mean of them
,Norms
2 ways of interpreting tests:
1. Criterion Referenced Testing = there is a specific criterion that needs to be met in order to
‘pass’ or ‘succeed’ in a particular testing situation
Involves A
bsolute Norms = norms needed to be set beforehand, independent of the test results
2. Norm Referenced Testing = designed to compare and rank testtakers in relation to one another
Involves R
elative Norms = norms obtained from other people taking the same test
Norm Scores:
Z-Score =
shows the number of standard deviations any given score is from the mean
The mean has a standard score of 0 and a score that is one std. dev. from the mean is 1
Z-scores can also be negative, indicating std. devs. below the mean
Formula → Z x = X −X
Sx
- X = individual score of a person on the test
- X = mean score on the test
- Sx = standard deviation of the test
T-Score = a rewritten z-score → we convert z-scores into t-scores to gain a more intuitive set of
scores for a variable that we can communicate easily to people that do not know means or std. devs.
The mean score is set at 50 and the std. dev. is set at 10
Formula → T x = 10 * X Sx
−X
or
T x = 10 * Zx + 50
Percentile Score =
the % of people that obtained the same/lower score than any particular score
Cumulative Percentage= add the % of people with same score to the % of people with lower score
- High Percentile Score → indicates a high score
- Low Percentile Score → indicates a low score
COTAN = the organisation that routinely checks psychological tests in the Netherlands
You do not want to base your norms on a too small group and definitely not on a group from a few
decades ago, as these norms will likely not be representative of the population
, Week 2: Reliability
Classical Test Theory
Classical Test Theory (CTT) = a theory based on the idea that every observed score (Xo) consists
of a true score (Xt) and the measurement error of the instrument (Xe)
True Score = always a l atent score, we cannot directly observe it
Error = indicates difference between the true score and observed score
- Negative Error = when the true score is higher than the observed score
- Positive Error = when the true score is lower than the observed score
Formula → X o = Xt + Xe
Three specific assumptions in CCT:
1. μ e = 0 → the mean of the errors in the population is equal to 0
2. ret = 0 → the errors do not correlate with the true scores
3. reiej = 0 → the errors are independent and do not correlate with each other
a. All these assumptions ay that the errors have to be random, not systematic
The observed variance can be split in part true variance and part error variance. The rest is that the
observed variance (So2) is equal to the true variance of the scores (St2) and the variance of the error
(Se2) added together (= basically the same as before)
Formula → So2 = St2 + Se2
Reliability Coefficients
Reliability Coefficient = Rxx
St 2
Formula → Rxx = So 2
- St2 = true variance
- So2 = observed variance
The observed variance exists out of true variance and error variance. The more true variance there
is, therefore the less error variance there is, the more reliable our test is
- Reliability of 0.70 is good enough for research
- Reliability of 0.80 is good enough for individual diagnosis
