Chapter 9

Principles of Analysis and Interpretation

Principles of Analysis and Interpretation

• Data, as used in behavioral research, means research results from which inferences are drawn: usually numerical results, like scores of tests and statistics such as means, percentages, and correlation coefficients.

• Analysis means the categorizing, ordering, manipulating, and summarizing of data to obtain answers to research questions.

• Interpretation takes the results of analysis, makes inferences pertinent to the research relations studied, and draws conclusions about these relations.

Frequencies and Continuous Measures

• Quantitative data come in two general forms: frequencies and continuous measures.

• f={(x,y); where x is a member of the set X, and y is either 1 or 0 depending on x’s possessing or not possessing M}

• f={(x,y); x is an object, and y= any numeral}

Rules of Categorization

• The first setup in any analysis is categorization.• The five rules of categorization are as follows:• 1.Categories are set up according to the

research problem and purpose.• 2.The categories are exhaustive.• 3.The categories are mutually exclusive and

independent.• 4.Each category (variable) is derived from one

classification principle.• 5.Any categorization scheme must be on one

level of discourse

Kinds of Statistical Analysis

• Frequency Distributions• Graphs and Graphing• Measures of Central Tendency and Variability• Measures of Relations• Analysis of Differences• Analysis of Variance and Related Methods• Profile Analysis• Multivariate Analysis

Graphs and Graphing

• A graph is a two-dimension representation of a relation or relations.

• Figure 9.1, 9.2, 9.3

• Interaction means that the relation of an independent variable to a dependent variable differs in different groups or at different levels of another independent variable..

Frequency Distributions

• Although frequency distributions are used primarily for descriptive purposes, they can also be used for other research purposes.

• Observed distributions can also be compared to theoretical distributions (normal distributions).

Measures of Central Tendency and Variability

• Mean, median, mode

• Standard deviation, range

Measures of Relations

• Ideally, any analysis of research data should include both kinds of indices: measures of the significance of a relation and measures of the magnitude of the relation.

Analysis of Differences

• 1.it is by no means confined to the differences between measures of central tendency.

• 2.All analyses of differences are intended for the purpose of studying relation. Conversely, the greater the differences the higher the correlation, all other things being equal.

Analysis of Variance and Related Methods

• A method of identifying, breaking down, and testing for statistical significance variances that come from different sources of variation. That is, a dependent variable has a total amount of variance, some of which is due to the experimental treatment, some to error, and some to other causes.

• Figure 9.5, 9.6

Profile Analysis

• Profile analysis is basically the assessment of the similarities of the profiles of individuals or groups. A profile is a set of different measures of an individual or group, each of which is expressed in the same unit of measure.

Multivariate Analysis

• Multiple regression

• Canonical correlation

• Discriminant analysis

• Factor analysis

• Path analysis

• Analysis of covariance structures

• Log-linear models

Indices

• Index can be defined in two related ways:• 1.An index is an observable phenomenon

that is substituted for a less-observable phenomenon. For example, test scores indicate achievement levels, verbal aptitudes, degrees of anxiety, and so on.

• 2.An index is a number that is a composite of two or more numbers. For example, all sums and averages, coefficients of correlation.

Indices

• Indices are most important in research because they simplify comparisons. The percentage is a good example. Percentages transform raw numbers into comparable form.

• Indices generally take the form of quotients: ratios and proportions.

Social Indicators• Indicators, although closely related to indices—

indeed, they are frequently indices as defined above—form a special class of variables.

• Variables like income, life expectancy, fertility, quality of life, educational level (of people), and environment can be called social indicators. Social indicators are both variables and statistics.

• Unfortunately, it is difficult to define “social indicators.” In this book we are interested in social indicators as a class of sociological and psychological variables that in the future may be useful in developing and testing scientific theories of the relations among social and psychological phenomena.

The Interpretation of Research Data

• Adequacy of Research Design, Methodology, Measurement, and Analysis

• Negative and Inconclusive Results

• Unhypothesized Relations and Unanticipated Findings

• Proof, Probability, and Interpretation

Adequacy of Research Design, Methodology, Measurement, and Analysis

• Most important, the design, methods of observation, measurement, and statistical analysis must all be appropriate to the research problem.

Negative and Inconclusive Results

• When results are positive, when the data support the hypotheses, one interprets the data along the lines of the theory and the reasoning behind the hypotheses. If we can repeat the feat, the n the evidence of adequacy is even more convincing.

• If we can be fairly sure that the methodology, the measurement, and the analysis are adequate, then negative results can be definite contributions to scientific advancement.

Unhypothesized Relations and Unanticipated Findings

• The unpredicted relation may be an important key to a deeper understanding of the theory. For example, positive reinforcement strengthens response tendencies.

• Unpredicted and unexpected findings must be treated with more suspicion than predicted and expected findings. Before being accepted, they should be substantiated in independent research in which they are specially predicted and tested.

Proof, Probability, and Interpretation

• Let us flatly assert that nothing can be “proved” scientifically. All one can do is to bring evidence to bear that such-and such a proposition is true.

• Proof is a deductive matter. Experimental methods of inquiry are not methods of proof, they are controlled methods of bringing evidence to bear on the probable truth or falsity of relational propositions.

• In short, no single scientific investigation ever proves anything. Thus the interpretation of the analysis of research data should never use the word proof.