What is a correlational study? To find relationships between naturally occuring events, researchers use correlational studies measure one variable (X) measure a second variable (Y) determine a statistical relationship between the variables. Correlational studies MEASURE variables, they do not manipulate variables. Correlational Coefficient The correlation coefficient is statistical value that indicates the strength of the relationship between two variables. The mathematical representation for the correlation coefficient is r. Correlation(r) = ( N?
XY – (? X)(? Y) ) / Sqrt([N? X2 – (? X)2][N? Y2 – (? Y)2]) Correlation Coefficient: -1 < (or equal to) r < (or equal to) 1 Positive: – If x and y have a strong positive linear correlation, r i close to +1. – An r value of exact +1 indicates a perfect positive fit. – Positive values indicate a relationship between x and y variables such as values for x increases, values for y also increase. Negative – If x and y have a strong negative linear correlation, r is close to -1. – An r value of exactly -1 indicates a perfect negative fit. Negative values indicate a relationship between x and y such that as values for x increases, values for y decrease. Correlation Coefficient: -1 < (or equal to) r < (or equal to) No correlation: – not a linear relationship, but a curve – if there is no line correlation or a weak linear correlation, r is close to 0. – a value near zero means that there is a random, nonlinear relationship between the two variables. Coefficient of Determination: r^2 The coefficient of determination r^2 is useful because it gives the proportion of the variance (fluctuation) of one variable that is predictable from the other variable.
It is a measure that allows to determine how certain one can be in making predictions from a certain model/graph. The ratio of the explained variation to the total variation. 0 < r2 < 1, and denoted the strength of the linear association between x an dy. Represents the percent of the data that is the closest to the line of best fit. for example if r = 0. 922, then r2 = 0,850, which means that 85 % of the total variation in y can be explained by the linear relationship between x and y (as described by the regression equation). The other 15% of the total variation in y remains unexplained.
Correlational Studies Advantages Are relatively simple and provide a numerical representation that is easy to understand. Allow the study of a number of variables that cannot be manipulated experimentally. Disadvantages Impossible to make cause-effect conclusions Does x cause y? Does y cause x? Third variable problem (Z-variable problem) Does Z cause x and/or y? Some patterns are not represented linearly ( it doesn’t show on the correlation coefficient) U-shaped graph for example. Observational Studies A target behavior* is observed without manipulation of an independent variable.
Target behavior must have a clear operational definition. Observational Studies may vary along these types: Covert v. Overt Participant v. Non-participant Naturalistic v. Controlled Observations Advantages Allows researches to catch behavior as they authentically occur, with little artificiality. Data collected as the behavior occurs, making it possible to describe behaviors that might otherwise be difficult. Disadvantages Demand characteristics may be a problem and render result invalid (people behave differently when they know they are observed) Hawthorne Effect – alterations in behavior according to participants? xpectations about what is being studied. Audience Effect – exaggerations or concealment of behavior because of “being watched” Researchers Bias Biased in the selection of target behaviors Biased in the perceived frequently of those behaviors *bets avoided by using neutral observers Ethics Generally okay to observe behaviors for research that would normally be observed by other without getting informed consent, but… Recording Observational Data Grid (structured observation) Advantages are: Ease of recording data Standardization of recording data Disadvantages are:
Pre-prepared, therefore reflects researchers expectations (biases) Rich behaviors reduced to number (no context offered) Vague Data Recordation Protocols Advantages are: Allows for context and researchers thoughts to become part of the data Disadvantages are: Subjectivity of researchers (must be acknowledged and become part of the interpretation of the data) Reflexivity (researcher’s reflections on the process) should become part of the study and therefore are available for readers to evaluate in terms of trustworthiness and credibility of the study.
Analyzing Observational Data Quantitative Study When numbers of incidents are counted, as in structured observations, traditional quantitive analysis is appropriate (comparison od mean and mode values, eg. ) Qualitatively In unstructured observation, grounded theory, or analysis of emerging themes and coding them is appropriate. It is necessary to record the manner in which the analysis for themes and coding occurred so readers may evaluate for credibility and trustworthiness.