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Descriptive Statistics Used to describe or summarize sets of data to make them more understandable – measures of central tendency mean, median, mode – measures of variability range, standard deviation – measures of association correlation coefficient Measures of Central Tendency What is the average family income above? Mean - the arithmetic average – Total sum of all scores divided by the number of scores Median - the center score – 50th percentile score, half of the scores are above and half are below Mode - the score that occurs the most Measures of Variability (amount of variation in the data – how similar or diverse the scores are) Range - the difference between the highest and lowest score in a set of data – Not always reliable – extreme scores (outliers) can create a deceptively large range. Measures of Variability Standard deviation - reflects the average distance between every score and the mean – Better gauge of whether scores are packed together or dispersed – Large std. deviations signify that scores are more scattered, therefore the mean is not terribly typical Normal Distribution Normally distributed variables produce the familiar symmetric, bell-shaped curves obtained when large numbers of observations are made on a single variable Curves can be skewed in a positive or negative direction depending on the position of the long tail (outliers), not the position of the bulge Normal Distribution Skewed Distribution Measures of Association Correlation Coefficient Often we measure more than one variable – Grade point and SAT score Are they related? Correlation statistic is a way to find out Inferential Statistics Descriptive statistics summarize a data set We often want to go beyond the data Is the world at large like my sample? Are my descriptive statistics misleading? Inferential statistics give probability that the sample is like the world at large Statistics and Probability Probability means how likely something is How likely are results like mine to occur by chance? Statistical Significance How likely it is that a study’s results occurred by chance (t-test or chi-square test) – Statistically significant – reflects the real world rather than chance – p≤.05 A result would be considered significant if it would be expected to occur by chance 5 or fewer times in 100 repetitions of the study. – Not significant – results reflect chance – p≥.05 Inferential Statistics When is an observed difference reliable? Representative samples are better than biased samples. Less-variable observations are more reliable then those that are more variable. More cases are better than fewer. Sources of Bias Biased sample - when the members of a sample differ in a systematic way from the larger population the researcher is interested in Example – interested in all voters – contact by telephone – biased sample - lower economic groups may not own telephones Ethical Issues in Psychological Research Right to privacy Informed consent – use of deception Animal rights – Is there justification for discomfort or harm a research procedure may produce? APA publishes ethical guidelines