Levels of Measurement: Nominal = Data one collects when doing a wide-open descri

Levels of Measurement: Nominal = Data one collects when doing a wide-open descriptive or exploratory study, however, it is not limited to these kinds of studies. We can count this data, but we can’t order it. We need to be able to put this data into categories that are mutually exclusive, i.e. it can’t be in more than one category at a time. An example would be looking at age, race, sex, or some other type of data that you either are or aren’t. The categories need to be exhaustive – there need to be enough categories to cover the data you collect. Ordinal = this category has mutually exclusive categories, but with ordinal data you can order the data within each category. The ratings of poor, fair, good are an example of ordinal information. Note that you can order the ratings, but you can’t really tell how far apart each of these descriptors are from each other. You could also look at who finishes a task first, second, third, and so on. Again, you can rank this data, but you don’t know how much faster the first person was in relation to the second person or subsequent people. Interval-ratio data = this type of data allows you to measure the difference between each of your rankings. Data is ordered (as with ordinal data) and you can tell how much difference there is between each observation because there is a scale that is divided into equal units. You can measure a race with a stopwatch in terms of seconds or tenths of seconds. A thermometer gives you data with measurements in degrees. Ratio data is like interval data (and is often lumped together with it because they are usually handled the same way statistically). Its primary difference is that there is a zero point on the scale so that you can do multiplication and division. Money is an example of a ratio scale – two dollars are exactly twice one dollar. Volume, area, and distance measures are also ratio scales (2 times 1 liter equals 2 liters). This is different from a strict interval scale like a thermometer – we can’t say that 10 degrees Fahrenheit is twice as warm as 5 degrees Fahrenheit. Statistical Distributions: According to Shi, “a distribution organizes the values of a variable into categories. Frequency Distribution (aka Marginal Distribution): Displays the number of cases that falls into each category. Percentage Distribution: Found by dividing the number of frequency of cases in the category by the total N. Measures of Central Tendency: Mean: The most common measure of central tendency. It simply the sum of the numbers divided by the number of numbers. Median: It is defined as the middle position or midpoint of a distribution. Mode: Is defined as the most frequently occurring value. What is variability? Amount of spread or dispersion within a distribution of scores within a set of data. Measures of Variability: Range: The difference between the highest and lowest values in a distribution. Interquartile Range: Known as the ‘midspread’ or ‘middle fifty.” It contains the middle 50% of the scores in a distribution from a set of data. Variance: The average squared deviation from the mean. Standard Deviation: The square root of the variance. Measures of Shape: Two most common Skewed: The amount and direction apart of normal symmetry. If the bulk of the data is at the left and the right tail is longer, we say that the distribution is skewed right or positively skewed; if the peak is toward the right and the left tail is longer, we say that the distribution is skewed left or negatively skewed. (visit: http://www.tc3.edu/instruct/sbrown/stat/shape.htm) Kurtosis: The extent to which cases or observations cluster around a central point. Chi-Square: Tests for independence Compares an observed frequency and expected frequency. Can be used with nominal and ordinal (and other data) Used to determine if what we observe is significant in relationship to what we would expect to observe based on the entire sample. For example, let’s say we are looking at the number of students using the library. We survey 120 students and ask them how often they use the library (never, 1-2 times a week, 3-4 times a week, 5 or more times a week) and we want to know how men and women compare. We can easily tabulate this information: Women Men Total Never 7 (11.8) 17 (12.2) 24 1-2 times per week 24 (29.5) 36 (30) 60 3-4 times per week 19 (12.4) 6 (12.8) 25 5 or more times per week 9 (5.31) 2 (5.4) 11 Total: 59 61 120 The numbers in parentheses are what we expect based on the percent of the total sample going to the library times the number of total women or men surveyed. (I.e. for never, 20% of the total sample never go to the library, therefore 11.8 women or 12.2 men ‘should’ never go to the library based on the entire sample). We can then use Chi-square to figure out if these differences from the ‘expected’ are significantly different. **Chi-square is an example of a non-parametric test of significance. This means it can be used with nominal and ordinal data. You can get more sophisticated with interval and ordinal data. Types of Regression: Simple Regression: Examines the relationship between two interval-ratio-level variables. Multiple Regression: Examines the relationship among variables or to test hypothesis about population parameters. It is a statistical technique that predicts values of one variable on the basis of two or more other variables. Linear Regression: Analyzes the relationship between one or more independent variables along with another variable, the dependent variable. Logistic Regression: Has a dependent variable that is binary or dichotomous. A type of linear regression that predicts the proportions of a categorical target variable, such as type of customer, in a population. Shi, L. (2008). Health Services Research Methods (2nd Ed). New York: Thomson-Delmar Learning.