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Appendix: Statistics in Psychology Descriptive Statistics summarize and describe the characteristics of a set (also called a distribution) of scores Frequency Distribution is used to summarize a set of scores. It shows how many participants received each score. Histogram is a graph of a frequency distribution Measures of Central Tendency describe a distribution in terms of a single statistic that is in some way “typical” of the sample as a whole Mode is the most frequently occurring score in a distribution Mean represents the arithmetic average of a set of scores Median is the point that divides the distribution in half when the individual scores are arranged in order from lowest to highest Measures of Variability provide information about the spread of scores in a distribution Range is the difference between the highest and the lowest score in the distribution Is the simplest but least informative measure of variability Variance is the average of the squared deviation scores about the mean Standard Deviation (SD) is the square root of the variance Normal Curve is a symmetrical bell-shaped curve that represents a theoretical distribution of scores in the population, 50% of the cases fall on each side of the mean, and the median & mode have the same value as the mean

Accounting for Variance in Behaviour  

Explaining why variation in behaviour occur is a central goal of psychological science In any experiment, the total amount of variation in people’s behaviour may be divided into two components: o The amount of variance accounted for by the differences in the independent variable(s) being manipulated o The amount of variance that’s left over and therefore must be due to other factors. Thus, Total Variance = Variance accounted for + Variance not accounted for

Ex. Examined the effect the number of bystanders present during an emergency effects the speed at which they assist. The number of bystanders is the independent variable and the speed of helping is the dependent. The experiment reveals 20% of the total variance in the speed can be accounted for by the independent variable, while the other 80% of the variance in speed is due to factors not controlled in the experiment. Some of these factors produce an error variance. The rest of the unexplained variance can be attributed to things unknown to the researcher such as the participants personality, mood, gender, etc.

Correlational Methods  

Variance accounted for concept also applies to correlational studies Question: As variable X increases/decreases, does variable Y tend to increase/decrease in a systematic manner? Is there a relation in their variances?

The Correlation Coefficient  Relations between variables can differ in direction (+/-) and in strength A relation is positive in direction when higher scores on variable X are associated with higher scores on Y, or when negative X is associated with negative Y. A relation is negative in relation when higher X scores are associated with lower Y scores and vice versa The Pearson Product-Moment Correlation Coefficient is a statistic that reflects the direction and strength of the relation between two variables  the correlation coefficient can range in magnitude from -1.00 to +1.00, with r= -1.00 reflecting a perfect negative relation between X&Y and r= +1.00 a perfect positive relation  Correlations close to 0.00 indicate no systematic relation between the variables  Remember it’s the magnitude not the sign that indicates the degree which two variables are related o X & Y are more strongly related when r = -0.75 than when r= +0.58  The amount of variance two variables has in common is indicated by squaring the correlation coefficient (r2) o Ex. There’s a correlation of +0.50 between scores on a mechanical aptitude test and grades in a university course. +0.502 = 0.25, telling us that 25% of the total variance in grades can be accounted for by differences in mechanical appt scores Correlation and Prediction  If two variables are correlated and we know an individual’s score on one variable, we can estimate his or her score on the other variable  The more highly two variables are correlated, the more accurate our predictions will be Factor Analysis a statistical technique that reduces a large number of correlations among many measures to a smaller number of clusters, with each cluster containing variables that correlate highly with one another 

Inferential Statistics and Hypothesis Testing Inferential Statistics tell us how confident we can be in drawing conclusions or inferences about a population based on findings obtained from a sample Statistical Significance means that it is unlikely the particular finding occurred by chance alone Null Hypothesis states that any observed differences between the samples are due to chance...