1. PPA 501 – A NALYTICAL M ETHODS IN A DMINISTRATION Lecture 3b – Fundamentals of Quantitative Research

2. I NTRODUCTION A key objective of most public administration and nonprofit organization research is to improve the quality of decisions made by managers and administrators. To make effective managerial decisions, administrators must know how to use quantitative research methods and how to interpret quantitative data. The proper use of numbers can make communicating easier, faster, and often more effective than the use of words alone. These numerical data are called statistics.

3. F UNDAMENTALS OF M EASUREMENT Nominal data. Categories – different numbers must mean different things. Ordinal data. Categories. Ranked – the things can be ranked on some scale. Interval data. Categories. Ranked. Equidistant interval – The differences between ranks must be measured in equal or measurable intervals. Ratio data. Categories. Ranked. Equidistant interval. Absolute zero – The zero point must mean the absence of the phenomena under investigation. For most social science data, interval and ratio data are the same. Generally, both are referred to as “scale” data.

4. S TATISTICAL T ERMS AND C ONCEPTS Descriptive statistics: Measurements or numbers used to summarize or describe data sets. Inferential statistics: Statistical techniques used to make estimates or inferences about the characteristics of interest for a population using the data from a sample data set. Sample: A portion of a population. The sample is chosen as representative of the entire population. Population: The set of all elements for which measurements are possible. A population can consist of products, workers, customers, firms, prices, or other items about which the decision maker or manager is interested. Another word used to identify a population is a universe.

5. S TATISTICAL T ERMS AND C ONCEPTS Statistic: A number used as a summary measure for a sample. For example, "The mean age for the 20 students in the sample is 20.3 years." Parameter: A numerical value used as a summary measure for a population or universe. For example, in the statement "The mean age for all entering college or university freshmen is 19.1 years"; the age of all entering freshmen is a parameter Variable: A characteristic or quantity that can have different values. Examples include savings account amounts, stock prices, package designs, weight, monthly sales, gender, and salaries. The values of variables may be said to be either continuous or discrete. Continuous Variables: Quantities that are measured, such as weight or percentage of increase in the price of a stock, are said to be continuous. Values for these variables can be measured on a continuous scale, such as weights, and are not restricted to specific, discrete categories or values.

6. S TATISTICAL T ERMS AND C ONCEPTS Discrete variables: Variables with values that can vary only in specific steps or categories (they are sometimes called categorical). Assuming that we assign in advance the value of 1 for female and 2 for male, the variable gender is an example of a discrete variable. Univariate statistics: Statistics describing a single variable. They include such measures as the valid number of responses (frequencies); the mean, median, and mode; and standard deviation. Bivariate statistics: Measurements with which two variables are described or compared at the same time. A crosstabulation table is an example of bivariate statistics in use. Counts, percentages, correlations, difference tests, and many other statistical tests can be carried out with bivariate statistics. Multivariate statistics: Statistics, such as multiple regression analysis, used when more than one independent variable influences one dependent variable. For example, sales of a product are probably influenced by aesthetics, price, availability (distribution), and advertising.

7. S OME C ATEGORIES OF S TATISTICS Descriptive statistics. Numerically describe events, concepts, people, work, or many other things. Summarize a set of data. Inferential statistics. To make generalizations about a larger group—called a population—from which the sample was drawn. To make estimates or draw conclusions about the characteristics of a population. To make predictions about some future event or state of affairs.

8. S OME C ATEGORIES OF S TATISTICS Parameters versus statistics. A parameter is a summary measure for a population or universe. A statistic is a summary measure for a sample. Parametric versus nonparametric statistics. Parametric statistics require that measurements come from a population (rather than a sample) where the distribution of variances is normal. Nonparametric statistics must be used when the data are nominal or ordinal. No assumptions are made about the distribution or the population.

9. D ESCRIPTIVE AND I NFERENTIAL S TATISTICS Descriptive statistics. Measures of central tendency (mean, median, mode). Measures of variability (standard deviation, range, interquartile range). Measures of relative position in the set (percentiles, standard scores). Measures of correlation between two or more variables (association, correlation coefficients). Inferential statistics. Independent samples t-tests. Dependent samples t-tests. Correlation and regression analysis. One-way analysis of variance. Two- or n-way analysis of variance. Analysis of covariance. Simultaneous equation modeling.