1. What are the scales of measurement? Descriptive statistics are included in the Analysis of Data section. There are two types of statistics. Descriptive describes what it sees, and inferential infers its results to a larger population. The scales of measurement define the types or groupings of categories and can be nominal, ordinal, interval, or ratio.

2. How do the scales of measurement differ from one another? The scales of measurement are (1) nominal scale (grouping categories based on names, such as 1, 2, or 3, where the names do not have a special meaning, and the only intent is to categorize), (2) ordinal scale (transitivity property such that if a>b and b>c, then a>c; a grouping by order or category, involves ranking people in an order but is low scale because the groups or names are not significant (in a race, the first 3 may be very close but the 4th finisher may be very far behind)), (3) interval scale (allows intervals which can be added and subtracted (98 degrees - 95 degrees = 3 degrees) but not multiplied or divided because interval data has an artificial zero (0 degrees Fahrenheit is not a total lack of heat)), and (4) ratio scale (has all qualities of interval scale and zero really is zero). NOTE: Is a zero on a math test interval or ratio. It is only ratio if the test truly shows a complete lack of math knowledge.

3. What are the characteristics of each measure of central tendancy? The measures of central tendancy are: (1) mode (the score that occurs most often but does not tell the researcher anything about the results), (2) median (the middle score which leads one to be ordinal rather than just looking at the mode but still does not tell the researcher very much), and (3) mean (arithmetic average which is either interval or ratio type of data because it takes into account everyone, can be added/subtracted, and allows the researcher to look at the sample around the average.

4. What are the measures of variability? Variance is the sum of the differences squared and divided by the number of observations. Standard deviation is the square root of the variance. Skewness occurs when the sample varies from a normal bell curve distribution. The direction of the tale determines whether the skewing is positive or negative. If everyone did very poorly on a test, then the sample would be positively skewed. Skewness is based on how people are placed in the entire sample.

5. What are the characteristics of the normal curve? The probabilities of a normal curve can be easily determined by use of the standard deviation. For example, 68.26% of all the observations will be contained in a range of the mean plus or minus 1 standard deviation, 95.44% are within plus or minus 2 standard deviations, and 99.74% will be contained within the mean plus or minus 3 standard deviations.

6. What is the purpose of standard scores? The standard score helps a researcher look at different individuals across multiple tests and determine who has scored best. For example,

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Person 1 scores 60 on test 1 (with a mean=70 and standard deviation=10). Their standard score will be (60-70)/10 = -1.0.

Person 2 scores 75 on test 2 (with a mean=60 and standard deviation=5). Their standard score will be (75-60)/5 = 3.0.

Person 3 scores 85 on test 3 (with a mean=70 and standard deviation=10). Their standard score will be (85-70)/10 = 1.5.

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Even though person 3 scored higher quantitatively, person 2 had a better standard score.

7. What does correlation indicate? Correlation shows how two variables relate to each other. They can be positively or negatively correlated. Perfect correlation occurs when the sample is perfectly correlated, but note the following: (1) correlation shows relationship, not causation, (2) coefficient is a function of variability, (3) coefficient is not a percentage of perfection, and (4) coefficients are not absolute across multiple tests.

				Tom of Bethany

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Lesson 13. Inferential Statistics

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