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What are the 3 properies associated with scales of measurements?
magnitude, equal intervals, and an absolute 0
Scales of Measurements: Magnitude
"Moreness". Instance of the attribute represents more, less, or equal amounts of the given quantity than does another instance. eg. John is taller than Fred. A scale that does not have this property arises, for example, when a gym coach assigns identifi cation numbers to teams in a league (team 1, team 2, and so forth). Because the numbers only label the teams, they do not have the property of magnitude. If the coach were to rank the teams by the number of games they have won, then the new numbering system (games won) would have the property of magnitude.
Scales of Measurements: Equal Intervals
A scale has the property of equal intervals if the diff erence between two points at any place on the scale has the same meaning as the diff erence between two other points that diff er by the same number of scale units. For example, the diff erence between inch 2 and inch 4 on a ruler represents the same quantity as the difference between inch 10 and inch 12: exactly 2 inches.
Can be a straight line or linear equation Y=a+bX
Scales of Measurements: Absolute 0
An absolute 0 is obtained when nothing of the property being measured exists. eg. no heartrate at 0 person dead.
4 Scales of Measurements
4 Scales of Measurements Nominal
- classification or grouping. Examples: gender, race,random assignment of groups.Nominal data has none of the
- three properties.
4 Scales of Measurements Ordinal
- ranking of individuals or variables.E.g., college football rankings. has magnitude, no equal intervals or absolute zero
- much of psychological data collected at ordinal level.
4 Scales of Measurements Interval
equal intervals between any two observations.e.g., temperature on the Fahrenheit or Celsius scales. has magnitude and equal intervals, no absolute zero.
4 Scales of Measurements ratio
- scale has all three properties. Examples: length of a field goal in football. 50 vs. 25 yards, rate of speed-70 vs. 35 mph
- a ratio scale of temperature would have the properties of the Fahrenheit and Celsius scales but also include a meaningful 0 point.
How are descriptive stats different from inferential stats?
– allow for concise description of a data set. measures of central tendency range of scores. Methods used to provide a concise description of a collection of quantitative information.
- (2) Inferential – use smaller representative sample to draw conclusions about larger group.Inferential statistics are methods used to make inferences from observations of a small group of people known as a sample to a larger
- group of individuals known as a population.
Typically, the psychologist ants to make statements about the larger group but cannot possibly make all the necessary observations. Instead, he or she observes a relatively small group of subjects (sample) and uses inferential statistics to estimate the characteristics of the larger group.
Measures of Central Tendency
Help to summarize main features of a data set
Allow for identification of the score around which most other scores fall
Measures of Central Tendency Name
(1) Mean – arithmetic average of all scores within data set. Affected by magnitude of every score. Mean = value for each individual if all shared equally.
2) Median – point that separates distribution into equal-sized halves. nmedian is not affected by the magnitude of every score.i.e., unaffected by extreme scores. median always = 50th percentile. median for even # of observations?
(3) Mode – most frequently occurring score. Considered to be least stable of all measures. infrequently used. Also not affected by extreme scores.
Measures of variability
CT only one piece, not sufficient to accurately describe distribution of scores. e.g., two data sets similar average scores but very different dispersion of scores around CT.
Missing piece = measure of how scores deviate or vary around CT. i.e., “variability” – allows for collective inspection of data set. homogeneity vs. heterogeneity of scores.
Measures of Variability name & define.
(1) range- depends solely on the two most extreme scores in the data set. crude statistic - not a dependable predictor of variability
(2) variance - average squared deviation around the mean. sum of the deviations around mean always = zero. square units to eliminate negative values. sum of squared deviations can then be calculated. widely referenced and valuable for statistical analysis. not a good descriptive statistic
(3) Standard deviation – square root of the variance. Much more useful in describing variability of a distribution. Small SD = homogeneity of scores within the group. Large SD = heterogeneity
Percentile Ranks vs. Percentile
- Percentile Rank- Percentage of scores that fall below particular score within distribution. To calculate:divide number of scores below
- score of interest by total number of scores-multiply result by 100. Measure of relative performance
- Percentiles are the specifi c scores or points within a distribution. Percentiles divide the total frequency for a set of observations into hundredths. Instead of indicating what percentage of scores fall below a particular score, as percentile ranks do, percen-tiles indicate the particular score, below which a defi ned percentage of scores falls.
***The percentile and the percentile rank are similar. Th e percentile gives the point in a distribution below which a specifi ed percentage of cases fall (6.75/1000 for Israel). Th e percentile is in raw score units. Th e percentile rank gives the percentage of cases below the percentile.
Types of norms:
- Allow for evaluation of one’s performance relative to larger group. e.g., student receives score of 17 on his spelling test
- What does this mean? What other information needed?
CT measures percentile ranks, standard scores provide information about one’s performance relative to comparison group.
Example: 3-year-old boy - 35 inches, 40lbs:Is he tall, heavy, etc? Is weight commensurate with height? Examples of age-related norms.
- “Norms” are not “standards”
- Norms – based actual performance measure of “what is”. no preconceived performance expectations.
- Norms should be current, relevant, and representative of the group to which the individual is being
- Standards – represent predetermined level of performance to be reached. measure of “what is desired” or
- “what ought to be”.
Why is it useful to transform raw score data to standardized scores.
Allow for more objectivevcomparisons. The Raw scores that are converted to fixed mean and standard deviation don't convey enough info to make meaningful assessments or accurate interpretations. Standard scores give more exact interpretations. The z score transforms date into standarized units that are more easily interpreted. eg. Grades on a test rated in terms of raw scores such as the number of items correct on a test. Z score gives feedback on performance by your professor would subtract the average score (mean) from your score and divide by the standard deviation. If your Z score was positive, you would immediately know that your score was above average; if it was negative, you would know your performance was below average.
Different types of standardized scores.
T-score (or “McCall’s T”):
- Z-score - foundation upon which all other standard scores are created. Transforms data into standardized
- units that are easily interpreted.
- * To calculate Z-score: (1) find difference between observed score and mean for the distribution. (2) divide difference by standard deviation of the distribution. Result is the number of standard deviation units above/below the mean.
- *Mean Z-score always = zero SD always = 1.0 Converting Z-scores to other standard scores: e.g., to percentile ranks –
- Appendix 1 in book (pp. 634-5)
Standard score procedure - sets mean at 50 with SD of 10 T-score = 50 + 10z Eliminates negative scores and decimal fractions.
Norm vs. Criterion based tests.
- each test-taker compared with a norm ntypically used for the purpose of making comparisons with a larger group.
- Criterion-referenced - specific skill/ ability / task that test-taker must be able to demonstrate e.g., test of math skills
- purpose is more idiographic.
Identify properties of skewed and normals distributions. How are measures of CT affected by a skewed distribution?
= bell shape (symmetrical); mean, median, and mode = same value
- Skewed distribution -observations heavily distributed to one side of curve
- *Positive” skew = tail points in positive direction
- *Negative” skew = tail points in negative direction
which CT measure is most impacted by collection of scores? which represents the “middle score?” which represents frequent occurrence?
Why do we need stats?
(1) summarize data E.g., what does a particular result mean?
(2) make judgments about events that can’t be observed directly
Why do we need stats?
- (1) summarize data
- E.g., what does a particular
- result mean?
(2) make judgments about events that can’t be observed directly