week 12

OLP 4404-5504: Evaluation in Corporate and Professional Technical Education 1

A Little Bit About Quantitative Statistics

Types of Statistics Descriptive statistics Used to organize and describe a set of data.

Inferential statistics Used to make inferences from a smaller group to a larger

group (a sample to a population). If used, generally used after descriptive statistics, not in lieu of them.

Levels of Data (Kinds of Measurement)

Interval (ratio) data Data can be placed into order and the distance between the items are consistent which means they can be used in calculations. (ex: thermometer)

Ordinal data Data can be ranked. You can say that one item is bigger or better (or more something) than the other, but you can not say how much bigger or better as the distance between points is not consistently measurable. (example of this: Likert scale)

Nominal data Used to categorize groups. Even if a “number” is used…this is a number that substitutes for a name and can not be used for calculations (for example: Departments 1, 2, and 3)

OLP 4404-5504: Evaluation in Corporate and Professional Technical Education 2

Common Descriptive Statistics Frequency (how many) Frequency Number of occurrences

Frequency distribution

Shows data in a manageable form counting the number of occurrences of a value and assigning it to the appropriate category. Examples:

Putting "tic marks" or totals in a table

Frequency graph:

Frequency Table Generally called a Contingency Table or Cross-Tabulation (cross-tab) because it shows the frequency of two or more variables at the same time.

A contingency table is a matrix that shows the frequency of data according to two variables (generally nominal/categorical, scaled variables). In the contingency table below (Table 1), the variables are satisfaction and gender.

Table 1. Satisfaction ratings by gender Low

satisfaction Medium satisfaction

High satisfaction

TOTALS

Females 2 7 23 32 Males 8 4 12 24 TOTALS 10 11 35 56

OLP 4404-5504: Evaluation in Corporate and Professional Technical Education 3

Measures of Central Tendency Mean The arithmetic average. Calculated by adding all the values and

dividing by the number of values.

Median The physical midpoint in a set of data. If you line up all the data from lowest to highest, this is the physical middle number in the lined up data. 50% of the values fall above the median and 50% of the values fall below the median.

Mode The value that occurs most frequently.

OLP 4404-5504: Evaluation in Corporate and Professional Technical Education 4

Measures of Variability (variability measures the spreadout-ness of the data) Range Distance between the lowest and highest scores.

Standard deviation (SD)

Represents the average amount of variability in a set of scores. (Average distance from the mean.) Most commonly used measure of variability. The larger the standard deviation, the larger the distance from the mean. Indicates the “spread-out-ness” of the curve when plotted.

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Common Inferential Statistics Correlation Correlation coefficient r (Pearson’s r)

Measure of the degree of relationship between two variables, ranging from .00 (no relationship) to 1.0 (perfect correlation). Plus (+) and minus (-) indicate the direction of the relationship. Interpreting a correlation Coefficient .8 to 1.0 Very strong relationship .6 to .8 Strong relationship .4 to .6 Moderate relationship .2 to .4 Weak relationship 0 to .2 Weak or no relationship

Coefficient of determination r2 (Variance accounted for)

Created by squaring the correlation coefficient. Indicates the amount of variance that can be explained. (Ex: the correlation between x and y is .7; r=.7 ; r2=.49 49% of the variation in X can be explained by Y)

Correlation matrix The way you typically display correlational relationships between more than one variable. (see sample matrix below in Table 2.) Table 2. Correlation matrix of income, education level, attitude, and voting Income Educ Attitude Vote Income 1.000 0.574 -0.080 -0.291 Educ 0.574 1.000 -0.149 -0.199 Attitude -0.080 -0.149 1.000 -0.169 Vote -0.291 -0.199 -0.169 1.000

Data on table 6 from: Salkind, n. J. (2005). Statistics for people who (think they) hate statistics. Thousand Oaks, CA: SAGE Publishing.