Lesson One: Terminology for statistics in educational research

ABC's of Statistics

Qualitative Versus Quantitative Research

1. Qualitative Research - data typically in narrative form; gathered by use of observations and interviews; results contextual - unique to individual and setting.
2. Quantitative research - data numerical; gathered by quantifying observations, administering tests and other instruments; results generalizable - attempts to find laws, generalizations.
3. Measurement - assigning numbers to observations according to rules.
4. Variables - a measured characteristic that can assume various values or levels.
5. Discrete variables - have only certain values (whole numbers for example).
6. Continuous variables - can take any value (accuracy of measurement).
7. Constants Constant - has only a single value. A certain characteristic (like grade level) can be a variable in one study and a constant in another study.

Scales of Measurement

1. Nominal scale - naming, used to label, classify, or categorize data (gender, SSN, number on athletic jersey, locker number, address).
2. Ordinal scale - classification function plus observations are ordered, distance between adjacent values not necessarily the same (olympic medals, finishing place in a race, class rank).
3. Interval scale - classification, ordered plus equal intervals between adjacent units (all test scores are assumed to be at the interval scale, temperature Fahrenheit, temperature Centigrade).
4. Ratio scale - all of the above plus the scale has an absolute zero, a meaningful zero. Most physical measures are at the ratio level of measurement (height, weight, distance, time, pressure, temperature on the Kelvin scale - absolute zero is -273 degrees Centigrade).

Descriptive and Inferential Statistics

1. Descriptive statistics are a way of summarizing data - letting one number stand for a group of numbers, can also use tables and graphs to summarize data.
2. Inferential statistics - research statistics, a measure of the confidence we can have in our descriptive statistics, the statistics we use to test hypothesis.

Parametric and Nonparametric Statistics

1. Parametric statistics - used with interval and ratio data and usually with data that were obtained from groups randomly assigned, normally distributed, and with equal variability between groups - preferred statistics to use, they are more "powerful" than nonparametic statistics. Examples we will study are t-tests, analysis of variance, and Pearson correlation coefficient.
2. Nonparametric statistics - used with nominal and ordinal data and sometimes with interval and ratio data when other assumptions can not be met. Examples we will study are the chi-square test and the Spearman rank difference correlation coefficient.

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