Descriptive Statistics and Inferential Statistics

AgendaData PreparationDescriptive StatisticsInferential Statistics

Data PreparationLogging the Data Checking the Data For AccuracyData Transformations

Descriptive StatisticsUnivariate Analysis Accesses properties of a single variableDistributionCenterSpreadCorrelation Shows ties between variables

Univariate Analysis (distribution)

Univariate Analysis (Center)Mean

Non-stable to extreme observationsVery useful in case of a normal distributionMedian

Great for visual comparison between distributionsVery useful in case of skewed distributionMode

Most frequent value in the distribution

Univariate Analysis (Spread)5 number summaryMin smallest observationQ1 median of the first half of a distributionMedian median of a distributionQ3 median of the second half of a distributionMax biggest observation

1.5 IQR rule

Univariate Analysis (Spread cont.)Standard DeviationShows relation of observations to the mean of a distributionCalculate a distance to mean for each valueSquare the results Divide a sum by the size of a distribution 1 (variance)Take a square root from variance

Univariate Analysis (Spread cont.)Standard DeviationEmpirical ruleapproximately 68% of the scores in the sample fall within one standard deviation of the mean approximately 95% of the scores in the sample fall within two standard deviations of the mean approximately 99% of the scores in the sample fall within three standard deviations of the mean

CorrelationNeed to determine whether there is a relationship between variables

Correlation (cont.)MagnitudeDirection

Correlation (cont.)Calculation

Test significance of produced valueSignificance levelDegree of freedom

Correlation (cont.)Situations when there is only 1 variable in the model are rare in real life. Need to compute correlation matrix.

Inferential StatisticsUsed for drawing conclusion about the population from a sampleEstimationEstimate true value of the parameter from a sampleHypothesis testingDetermine if there is a difference in a parameter value for two groups.

Inferential Statistics (General linear model )General linear model family of statistical models that produce most of inferential statistics

y = b0 + bx + e y outcomeb0 interceptx predictorsb coefficient estimatese error component

Inferential Statistics (General linear model cont.)Foundation for many statistical analysest-testChecks if means of two groups are different from each other on defined confidence levelANOVAChecks if there is a difference between more than two groupsANCOVAAdjusts the use of ANOVA by including covariates into the analysisRegression analysisCreates a model for predicting dependent variable

Inferential Statistics (Dummy variables.)Define different groups.

Research designExperimental Analysis. Quasi-Experimental Analysis.