Chapter 5: Alternatives to Experimentation

Correlational study

• is one that is designed to determine the ___, or degree of relationship, between two traits, or events.

• to explore behaviors that are not yet well understood.

Variable

• is any observable behavior, characteristics or event that can vary or have different values.

Pearson Product Moment Correlation Coefficient

is the most commonly used procedures for calculating simple correlations.

Weak

Determine the strength of relationship: 0.10 - 0.30

Moderate

Determine the strength of relationship: 0.40 - 0.60

Strong

Determine the strength of relationship: 0.70 - 0.90

Significant

p value is less than the alpha level p < 0.05 - the relationship is

Scatterplots/graphs/grams

visual representations of the scores belonging to each subject in the study.

Regression lines (lines of best fit)

they illustrate the mathematical equation that best describes the linear relationship the two measured scores. The direction of the line corresponds to the direction of the relationship.

No relationship

when the correlation (r) is near zero, you can say that there is ____ between variables.

Range truncation

Correlation coefficients are also affected by ___ (range restriction), an artificial restriction of the range of values of X and Y (variables).

Extreme scores

Another that can affect correlation coefficients is the presence of outliers

Coefficient of determination r²

• Once r is calculated, it is useful to compute the

• estimates the amount of variability in scores on one variable that can be explained by the other variable – an estimate of the strength of the relationship between them.

Bidirectional relationship

refers to a connection or interaction where two variables influence each other in a reciprocal manner, meaning changes in one affect the other and vice versa. 

Third-variable problem

arises when a correlation between two variables (X and Y) is actually due to a third, unobserved variable (Z) influencing both, leading to a misleading interpretation of a causal relationship. 

Mahalanobis distance

• takes into account the scale, correlation, and shape of the variables, and it is invariant to linear transformations.

• It is especially useful for detecting outliers, because it measures how many standard deviations a point is from the mean along each principal component.

Pearson’s R

Determine the statistical test: 2 continuous variable

Biserial correlation

Determine the statistical test: 1 artificial 1 continuous

Point-biserial correlation

Determine the statistical test: 1 true variable 1 continuous

Tetrachoric coefficient

Determine the statistical test: 2 artificial variable

Phi coefficient

Determine the statistical test: 1 true variable and 1 artificial ; 2 true variable

True variable

• in nature variable (e.g sex)

Artificial variable

• fictitious

• we do it ourselves (pass or fail in test)

Chi-square

• Determine the statistical test: 2 nominal variables

• determines if a sample's observed distribution of a categorical variable significantly differs from an expected distribution.

Linear regression analysis

is a correlation-based method for estimating a score on one measured behavior from a score on the other when two behaviors are strongly related.

Regression equation

is a formula for a straight line that best describes the relationship between the two variables.

Discrimination function analysis

• explores the predicting ability of the IV on one categorical DV

Multiple correlation

statistical intercorrelations among three or more behaviors, represented by R.

Partial correlation

an analysis that allows the statistical influence of one measured variable to be held constant while computing the correlation between the other two measured variables.

Multiple regression

a correlation-based technique (from multiple correlation) that uses a regression equation to predict the score on one behavior from scores on the other related behaviors.

Beta weights

Regression equations determine the weight of each predictor, and we could simply report these weights called

Factor analysis

• a common correlational procedure that is used when individuals are measured on a large number of items; allows us to see the degree of relationship among many traits or behaviors at the same time.

• is commonly used in personality research.

• determines the factors and sorts items according to their groupings in the different factors.

Factor loadings

statistical estimates of how well an item correlates with each of the factors (they can range from -1.00 +1.00).

Eliminate the item

factor loadings - <0.04 and variances - less than 8%

Exploratory Factor Analysis

• is used when the researcher wants to explore the relationships between variables and identify potential underlying factors or dimensions. 

Confirmatory Factor Analysis

• is used when the researcher has a pre-specified model or hypothesis about the relationships between variables and wants to test whether the data supports that model.

• For validation

Path analysis

• a correlation-based method in which subjects are measured on several behaviors; the researcher creates and tests models of possible causal sequences using sophisticated correlational techniques.

• uses beta weights to construct path models, outlining possible causal sequences for the related behaviors. Computers can easily compare many multiple regression equations testing different paths, looking for the best model.

Cross-lagged panel design

a method in which the same set of behaviors or characteristics are measured at two separate points in time (often years apart); the scores from these measurements are correlated in a particular way, and the pattern of correlations is used to infer the causal direction.

Quasi-experimental design

often seem like a real experiment, but they lack one or more of its essential elements, such as manipulation of antecedents and random assignment to treatment conditions.

Ex post facto study

• a study in which a researcher systematically examines the effects of pre-existing subject characteristics (often called subject variables) but without actually manipulating them. The researcher forms treatment groups by selecting subjects on the basis of differences that already exist.

• “after the fact” in effect, the researcher capitalizes on changes in the antecedent conditions that occurred before the study.

• has no direct control over who belongs to each of the treatment groups of the study (low high portion of the graphing scale).

Age and gender

two commonly research subject variables.

Nonequivalent group design

• a study in which the researcher compares the effects of different treatment conditions on preexisting groups of participants.

• The researcher cannot exert control over who gets each treatment because random assignment is not possible.

Longitudinal design

a method in which the same group of subjects is followed and measured at different points in time; a method that looks for changes across time.

Cross-sectional study

a method in which different groups of subjects who are at different stages are measured at a single point in time.

Pretest/Posttest design

a method that may be used to assess whether the occurrence of an event alters behaviors; scores from measurements made before and after the event are compared.