Statistical Analysis Quantitative research is first and foremost a logical rather than a mathematical (i.e., statistical) operation Statistics represent an efficient language for accomplishing the logical operations of data analysis

Looking at a dataset

Descriptive Statistics Statistical computations describing the characteristics of a sample Summary information for each variable in sample data set Used in more advanced statistical tests (inferential) to explore differences among and relationships between variables in order to generalize to the population

Frequency Distributions A description of the number of times the various attributes of a variable are observed in a sample (pg. 192) Ideal for categorial variables

Contingency Tables A format that allows us to see how frequences for one variable are contingent on, or relative to, frequencies for another variable (see pg 201) Two categorical variables

Measures of Central Tendency Mean Arithmetic mean or average Most sensitive to extreme scores Median Middle of all scores on one variable Mode Score or scores that appear most often

Measures of Dispersion Describes the variability or spread of scores Should be reported with mean Range –Highest to lowest score Standard deviation or sd – shows how far the average score deviates (varies) from the mean –If sd = 0, all scores are the same –Larger the sd, the more the scores differ from the mean

Normal Curve (Probability Sampling Theory) As scientists over time and across disciplines have collected data from natural sources, they have discovered that frequency distributions of data sets tend to have particular shape – the “normal curve” A theoretical distribution of scores –Majority of cases distributed around the peak in the middle –Progressively fewer cases moving away from the middle –Symmetrical – one side mirrors the other

p. 190