Descriptive Statistics Used to describe or summarize sets of data to make them more understandable Used to describe or summarize sets of data to make them more understandable –measures of central tendency mean, median, mode mean, median, mode –measures of variability range, standard deviation range, standard deviation –measures of association correlation coefficient correlation coefficient

Measures of Central Tendency What is the average family income above? What is the average family income above? Mean - the arithmetic average Mean - the arithmetic average –Total sum of all scores divided by the number of scores Median - the center score Median - the center score –50 th percentile score, half of the scores are above and half are below Mode - the score that occurs the most 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 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 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 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 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 Often we measure more than one variable –Grade point and SAT score Are they related? Are they related? Correlation statistic is a way to find out Correlation statistic is a way to find out

Inferential Statistics Descriptive statistics summarize a data set Descriptive statistics summarize a data set We often want to go beyond the data We often want to go beyond the data Is the world at large like my sample? Is the world at large like my sample? Are my descriptive statistics misleading? Are my descriptive statistics misleading? Inferential statistics give probability that the sample is like the world at large Inferential statistics give probability that the sample is like the world at large

Statistics and Probability Probability means how likely something is Probability means how likely something is How likely are results like mine to occur by chance? How likely are results like mine to occur by chance?

Statistical Significance How likely it is that a study’s results occurred by chance 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. 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. Representative samples are better than biased samples. Less-variable observations are more reliable then those that are more variable. Less-variable observations are more reliable then those that are more variable. More cases are better than fewer. 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 Biased sample - when the members of a sample differ in a systematic way from the larger population the researcher is interested in Example 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 Right to privacy Informed consent Informed consent –use of deception Animal rights Animal rights –Is there justification for discomfort or harm a research procedure may produce? APA publishes ethical guidelines APA publishes ethical guidelines