Measures of Dispersion. Range. Variance. Standard deviation. Measures of Relationship. Range. Variance. Standard deviation.

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1 Measures of Dispersion Range Variance Standard deviation Range The numerical difference between the highest and lowest scores in a distribution It describes the overall spread between the highest and lowest scores It is a relatively unstable measure of variability (depends only on two observations) Very easy to compute Variance The mean of all squared deviations from the mean A quantity expressed in squared units Of little use in descriptive statistics Important in statistical inference Standard deviation The square root of the variance A rough measure of the average amount by which observations deviate on either side of their mean A measure of distance Value can t be negative Very good in its resistence to sampling variation Widely used in advanced statistics Measures of Relationship Correlation - A measurement of the degree of relationship between two variables - Visually represented with scattergrams (scatterplots)

2 Relationship between variables Postive relationship A relationship between two variables in which, as the value of one variable increases, the value of the other variable tends to increase also Negative relationship A relationship between two variables in which, as the value of one variable increases, the value of the other variable tends to decrease No relationship Lack of relationship. No regularity among the pairs of values of the variables Bivariate distribution: A distribution in which two scores are obtained from each subject Scattergram: A graph of a bivariate distribution in which the X variable is plotted on the horizontal axis and the Y variable is plotted on the vertical axis Positive correlation Negative correlation No correlation

3 Measuring correlation When both variables are measured on an interval or ratio scale - Pearson s r When one or both variables are measured on an ordinal scale (rank-ordered) - Spearman s rho Comparing groups Is the difference between the experimental and control groups... - large enough - consistent enough... to suggest that the populations represented by those samples would show the same effect? Comparing groups Differences between groups Differences within groups = Effect of IV + Error Variance Error Variance Is the ratio considerably greater than 1? Statistical significance Comparing groups tests Data measured on an interval or ratio scale (parametric tests) - t-test: 2 groups - ANOVA: 3 or more groups -... others Data NOT measured on an interval or ratio scale (nonparametric tests) Introduction to Experimentation and the Between-Groups ~ Chapter 6

4 Experiments vs. Correlational studies Experiment - investigation in which the researcher manipulates an IV to see if there are differences in the DV among equivalent groups of participants - it yields causal information Experiments vs. Correlational studies Quasi-experiment - a study in which an IV is manipulated but where the groups of participants are not equivalent - it may yield causal information Experiments vs. Correlational studies Correlational study - investigation that explores the effect of a subject variable on a DV is a correlational study - does not yield causal information Between-Groups Research Comparing groups - Experimental group(s) - Control group Between-Groups Research Requirements for an experiment to yield causal results - Groups must be originally equivalent - must be free of confounds Equivalent groups - random assignment of participants (to avoid selection bias) When IV is a subject variable - random assignment of participants is not possible - E.g., Age : Cross-sectional design

5 Internal validity and Confounds Internal validity - extend to which the design of an experiment ensures that the IV (and not other ones) caused a measured difference in the DV - Internally valid study: has no extraneous variables that would confound the results Confound - extraneous variable or other flaw in the research design that yields alternative explanations Possible Confounds (affecting internal validity) Experimenter bias & Demand characteristics - Single-blind procedure: participants (or experimenter) ignore in which group they are in - Double-blind procedure: neither participants nor experimenters know who is in what group Instrumentation effects Subject attrition (systematic & non systematic) Comparable treatment of groups Sensitivity of DV (e.g., ceiling and floor effects) The Within-Subjects ~ Chapter 7 Within-Subjects An investigation in which each participant receives each level of the independent variable at least once - Pretest posttest design (2 measurements) - Repeated measures design (multiple measurements) - e.g., Longitudinal design Within-Subjects Benefits Require fewer participants than betweengroups designs They take less time Subject variables remain constant across the experimental conditions Low level of error variance (more power)

6 Within-Subjects Disadvantages Susceptible to confounds caused by: - demand characteristics - carryover effects (order effects) - practice effects - fatigue effects - history effects - maturation effects - testing effects Order effects and Counterbalancing Counterbalancing: - presenting the experimental conditions to participants in different orders so that carryover effects can be controlled - complete W-S design - incomplete W-S design Order effects and Counterbalancing Complete W-S design - All the participants experience each experimental condition several times until they have each received all possible orders of the conditions - ABBA counterbalancing (2 exp. conditions) - Block randomization (3 or more exp. conditions) - e.g., ABC, CBA, BAC, CAB, ACB, BCA Order effects and Counterbalancing Incomplete W-S design - Each participant receives a unique order of the conditions at least once but does not receive all possible sequences of the conditions - random order with rotation - balanced Latin square

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