Research Design in Occupational Education Copyright 1997. James P. Key. Oklahoma State University Except for those materials which are supplied by different departments of the University (ex. IRB, Thesis Handbook) and references used by permission.
 MODULE S4 INFERENTIAL STATISTICAL TERMS Descriptive Statistics - Numbers used to describe information or data or those techniques used to calculate those numbers. Inferential Statistics - A procedure used to estimate parameters (characteristics of populations) from statistics (characteristics of samples). Population - All subjects or objects possessing some common specified characteristic. The population in a statistical investigation is arbitrarily defined by naming its unique properties. Parameter - A measurable characteristic of a population (µ). Sample - A smaller group of subjects or objects selected from a large group (population). Statistic - A measurable characteristic of a sample (x, s). Variable - A characteristic of objects or subjects that can take on different values. Qualitative Variables - Characteristics which vary in quality or value. Quantitative Variables - Characteristics which vary in quantity, amount, or size. Independent Variables - Characteristics which affect or cause the outcome of the experiment but do not measure the results. Dependent Variables - Characteristics which measure the effects or results of the experimental treatment or independent variable. Predictor Variables (x) - Measurable characteristics from which the criterion variable (y) can be estimated. Levels of Measurement Nominal Scale - This simplest type of scale provides the lowest level of quantification of the objects to be measured. A nominal scale simply sorts objects or classes of objects into mutually exclusive categories. The number simply names or categorizes the objects or subjects. Ordinal Scale - Permits the sorting of objects or classes of objects on the basis of their standing relative to each other. This scale not only categorizes but also ranks the objects on the basis of some criterion. Interval Scale - Indicates the exact relative position of individuals because this type of scale uses predetermined equal intervals. Ratio Scale - Highest level of measurement. In addition to having equal intervals, a ratio scale measures from an absolute zero. Hypothesis - A supposition (an educated guess) presumed to be true for the sake of subsequent testing. In educational research, hypotheses concern the existence of relationships between variables. Statistical Hypothesis (Ho: Null Hypothesis) - States that there is no (null) relationship between the variables under analysis. Research Hypothesis (Ha: Alternative Hypothesis) - A positive statement of the null hypothesis. It states that there is a relationship between the variables under analysis. Probability (p) - The chance of something happening under certain conditions. In other words, it is the likelihood of the occurrence of any particular form of an event, estimated as the ratio of the number of ways in which that form might occur to the whole number of ways in which the event might occur in any other form. Example: If an event can happen in "s" ways and fail to happen in "f" ways, and if each of these s + f ways is equally likely to occur, the probability of success in a single trial is p = s / (s+f)   Statistical Significance When a statistical test reveals that the probability is rare that a set of observed sample data is attributable to chance alone, this result is labeled as statistically significant. If two groups are so different that only one time in 1000 would we find such a difference by chance alone, the difference would be statistically significant. By statistically significant, it is meant that the observed phenomenon represents a significant departure from what might be expected by chance alone. The level of significance (alpha) is the probability of a Type I error that an investigator is willing to risk in rejecting a null hypothesis. Generally, it refers to the probability of the event occurring due to chance. If alpha = .01, it is likely that one time out of a hundred the event could occur due to chance. If you lower the significance level from .05 to .01, you decrease the probability of rejecting a true hypothesis but increase the probability of accepting a false hypothesis. A Type II error (beta) occurs when an investigator fails to accept the alternative hypothesis when in fact the alternative hypothesis was true. In other words, the null hypothesis was accepted when it was not true.   1. Define. Inferential Statistics Quantitative Variable Qualitative Variable Population Sample Statistic Parameter Statistically Significant Research Hypothesis Statistical Hypothesis Probability 2. Name and define the four levels of measurement. 3. What is level of significance?