the most frequent score or category
advantages of mode
- no calculations needed
- can be used with nominal data
- best bet ifyou want to absolutely right
Desiadvantages to mode;
- not unique, doesnt always exist
- no further manipulations possible
- cant combine 2 distributions and find new mode from old mode
middle value in a set of scores
Advantages of median
- always exists always unique
- minimum of arithmetic
- notaffected by extreme scores or cutoffs
Disadvantages of median
- little further manipulation possible
- cant easily find new median when combining 2 distributions of scores
- not as reliable as the mean
Important properties of the mean
- sum of the deviations from mean = 0
- balance point of distribution
Adv. of the mean
- further manipulation possible
Disadvantages of the mean
- unduly influenced by extreme scores
- calculations more time consuming than the others
add logarithms of the numbers to be averaged together, divide by number of numbers and then take the antilog
used in psychophisicsand should be used in averaging ratios or rates of change
the number of numbers divided by the sum of the recipricals of the scores
Choice reaction time = a+b(bits)
law predicts that you should get close to a straight lineif you convert number of choices into bits of information.
use the median
Obtained score =
"true" score + unsystematic measurement error
Classic test theoey
- 1. obtained score = true score + unsystematic measurement error
- 2. calculate variance due to unsys. measurement error
- 3. calculate variance of true scores
- 4. Assume: variance of obtained scores=variance of true scores
variance scores obtained from repeatedly measuringsubjects on the same characteristic - variance within each subject
variance of means obtained from each subject measuring subjects on the same characteristic - variance between subjects
gives an index of the consistency of a measure from one session to the next.
- give test, survey, ormeasure to the same group 2 different times and then calculate the correlation between the scores of each person taking the test the first time and the second time.
- Use Pearson Product Moment correlation coefficient
Parallel Forms reliability
gives an index of the results of2 tests constructed in the same way and from the same content area. Give 1 form of a tes to a group of people and then give another form of the same test to the same group at a later time.
Calculate the correlation between scores on the first form and the second form
Interitem (internal Cconsistency) reliability
gives an index of the consistency of results across items within a test
one version of this method is the split half reliability. A test is divided into 2 halves. A total score is calculated for each half and the correlation between the 2 halves of the test is calculated
gives a measure of the degree to which different raters orobservers give consistent estimates of the same phenomenon.
- Calculated because observers or raters are frequently inconsistent.
- If the data is continuous, it can be calculated by the Pearson Product moment corr. coefficient.
- Ifit is nominal, it may be calculated by determining the degree of agreement between 2 or more people.
increases with the number of possible values that can be reliably used
- reliability of a measurement or a test refers to the stability or consistency of values obtained from the test, usually over time.
- A reliable measure is accurate or precise in the sense that it is free from random or unsystematic errors of measureent
Random or unsystematic errors
on the average random errors cancel out over a large group of people or over repeated measurements of the same thing or person
do NOT average out over a group of people or over repeated measurements of the same person or thing
Unsystematic errors, random errors influence the _______ of a sest of scores but not the _______. Systematic errors influence the _________.
refers to the extent to which the test measures what it is supposed (purports) to or designed to measure
refers to the extent to which a test uses items representative of the area you are trying to measure
refers to the degree to which test scores correlate with some criterion of interst (some indirect and independent measure of what you are trying to measure)
- refers to the degree to which test measures a theoretical construct or trait
- It is the extent to which a test or a measure can be shown to measure a particular theoretical construct-conceptual variable (unobservable abstract trait or feature)
- 1. test produces "numbers" DISTINCT from that produced by a measure of another construct.
- 2. Based on accumulated evidence
Steps in studying validity
- 1. Define clearly characteristic or trait(construct)....Sensation seeking.
- 2. Correlate test with a variety of measures that should be positively, negatively, or not correlated with characteristic(the construct)
- 3. If this diverse body of evidence shows the appropriate pattern the researcher may conclude that the scale has construct validity. (not based on just a single correlation)
Measures of the spread or variation;
give an idea about the consistency of a set of scores
largest score - smallest score
Median absolute deviation (MAD)
- 1. find median of a set of scores
- 2. find deviation from median by subtracting median from each score
- 3. take absolute value of each deviation
- 4. find median of absolute deviations
Variance and Standard Deviation
- (Xi - M) find the deviation of each score from the mean
- (Xi - M)2 scuare each deviation from the mean
- Sum(Xi - M)2 sum the squared deviations from the mean = sum of squares = total squared distance that a set of scores is from the mean
- Sum (Xi - M)2
Divide by the number of scores=variance=mean square= average squared distance a set of scores spreads out from the mean
Divide by N - 1 to find;