1. Analysis of Research Data
Statistical Analysis of Research Data

2. Purpose of Statistical Analysis
To summarize
To explore the meaning of deviations in data
To compare or contrast descriptively
To infer that findings from the sample are indicative of the entire population
To examine causality
To predict
To test the proposed relationships in a theoretical model
To infer from the sample to a theoretical model

3. Elementary Descriptive Statistics
Univariate descriptive statistics – these describe and synthesize data from empirical observations
Averages and percentages
Frequency distributions
Cumulative frequencies
Bar graph – nominal or qualitative
Frequency histograms – ordinal, interval or ratio
Frequency polygons – ordinal, interval or ratio

8. Elementary Descriptive Statistics
Measures of central tendency
Mode – for nominal data – where scores fall most frequently
Median – for ordinal data – the point above which and below which 50% of the scores fall
Mean – for interval or ratio data – the sum of the scores/the number of scores

9. Elementary Descriptive Statistics
Measures of dispersion or variability – the degree to which subjects in the sample are similar to each other with respect to the critical aspect – the extent of inter-subject differences
Range – for nominal data – the highest number minus the lowest number
Inter-quartile range – for ordinal data - the range between the middle two quarters where 50% of scores lie
Semi-interquartile range – for ordinal data – half of the range of scores in which the middle 50% of the scores lie
Variance – for interval data - how much the score varies from the mean (the average of the sum of squares)
Standard deviation – for interval data – the average of the deviations from the mean (the square root of the variance)

10. Standard Deviations in a Normal Distribution

11. Two Distributions of Different Variability

12. Elementary Descriptive Statistics
Shapes of distributions
Symmetrical – two halves fold over on themselves – the normal curve. In order to compare the scores in one sample with the scores in another, mechanisms were developed to transform raw scores into standard scores
Non-symmetrical – skewed
Positively – long tail to right (personal income)
Negatively –long tail to left (age at death)

13. Examples of Skewed Distributions

14. Elementary Descriptive Statistics
Shapes of distributions
Modality – most distributions are unimodal, but if they have more than one mode, they are most often bimodal – having two peaks
Kurtosis – the degree of peakedness of the curve
Platykurtic
Mesokurtic
Leptokurtic

15. Elementary Descriptive Statistics
Bivariate Descriptive Statistics – where there are two variables
Contingency tables – a two dimensional frequency distribution – the frequency of two variables are cross tabulated
Correlation – can determine the direction of a relationship between two variables – can display data graphically by use of the scatter diagram

16. BIVARIATE GENDER OBAMA McCAIN TOTAL Male 43 (33.6) 85 (66.4) 128 (100)
Female
215 (52.2)
197 (47.8)
412 (100)
258 (52.2)
282 (47.8)
540 (100)

18. Various Relationships Graphed on Scatter Plots

19. Elementary Descriptive Statistics
In a positive relationship, the scores vary together in the same direction and the slope of the line is from the 0 point of each variable to the upper right corner
In a negative relationship, the scores vary inversely, in opposite directions with the 0 of the independent variable being at the upper left corner or high level of the dependent variable and dropping to the lower right corner of the graph
The most common correlational statistical technique is Pearson’s Product Moment Correlation Coefficient. The outcome of the formula is an “r” value which indicates the degree of relationship between the two variables with +1 equaling perfect positive correlation and –1 equaling perfect inverse correlation