1. REVIEW OF BASIC STATISTICAL CONCEPTS Kerstin Palombaro PT, PhD, CAPS HSED 851 PRIVITERA CHAPTERS 1-4

2. DESCRIPTIVE STATISTICS  Used to describe or summarize numeric observations  Makes sense of a set of scores or observations  Data are presented graphically, in tables or as summary statistics PRIVITERA CHAPTERS 1-4

3. INTERFERENTIAL STATISTICS  Procedures that allow us to interpret the meaning of data PRIVITERA CHAPTERS 1-4

4. STATISTICAL TERMS RELATED TO INTERFERENTIAL STATISTICS  Population-the set of individuals, items, or data of interest  Sample-a selection of individuals from a given population PRIVITERA CHAPTERS 1-4

5. EXPERIMENTAL METHOD  Experiment-any study that demonstrates cause  Experiments manipulate an independent variable (IV)  Experiments measure the effect of manipulating the IV on a dependent variable (DV)  Experiments must have the following three characteristics:  Randomization  Manipulation  Comparison PRIVITERA CHAPTERS 1-4

6. QUASI-EXPERIMENTAL METHOD  Lacks, randomization, manipulation or comparison  Typically has a quasi-independent variable  Lacks a comparison group PRIVITERA CHAPTERS 1-4

7. CORRELATIONAL METHOD  Examines the relationship between variables  Can determine if a relationship exists, but cannot demonstrate cause and effect PRIVITERA CHAPTERS 1-4

8. SCALES OF MEASUREMENT  Nominal scale-identifies something but provides no additional information  Ordinal scale-conveys order alone  Interval scale-has equidistant data points and no true zero  Ratio scale-has a true zero and equidistant data points PRIVITERA CHAPTERS 1-4

9. TYPES OF DATA  Continuous variable-can be measured at any place beyond a decimal point  Discrete variable-measured in whole or fractional units.  Quantitative variable-varies by amount and is measured numerically  Qualitative variable-often represents a label and describes nonnumeric aspects of phenomena PRIVITERA CHAPTERS 1-4

10. SUMMARIZING DATA  Frequency distributions summarize how often scores occur in a data set  Can be grouped or ungrouped  Cumulative frequency-distributes the sum of frequencies across a series of intervals  Relative frequency-describes the portion of data in each interval  Divide frequency by the total number of scores  Relative percent-multiple relative frequency by 100  Cumulative percent-distributes the sum of relative percents across a series of intervals PRIVITERA CHAPTERS 1-4

11. GRAPHING CONTINUOUS DATA  Can display frequency data graphically  Histograms-graphs that distribute the intervals along the horizontal scale and list frequencies along the vertical scale  Frequency polygon-dot and line graph where do it midpoint of each interval and line connects each dot  Stem-and-leaf plot-common digits to a set of scores used to the left and remaining digits used to the right  Useful with smaller data sets PRIVITERA CHAPTERS 1-4

12. GRAPHING DISCRETE VARIABLES  Bar charts-like histograms except bars are separated from each other  Pie charts-circular display to summarize relative percent of discrete and categorical data  Scatterplot-display of discrete data points used to summarize the relationship between two variables PRIVITERA CHAPTERS 1-4

13. MEASURES OF CENTRAL TENDENCY  Central tendency-statistical measures for locating a single score that is most representative of all of the scores in a distribution  Mean-the average of a set of scores  Weighted mean is the mean of a group of disproportionate scores or samples of scores  Median-the middle value in a distribution of data listed in numeric order  Not influenced by outliers  Mode-the score the occurs most frequently in a distribution PRIVITERA CHAPTERS 1-4

14. NORMAL DISTRIBUTION  Half of all scores fall above and half below the mean, median and mode  Distributions can have some degree of kurtosis  Distributions can be skewed  Positively skewed- a group of scores falls substantially above most other scores  Negatively skewed-a group of scores falls substantially below most other scores PRIVITERA CHAPTERS 1-4; Graphs from: Field, A. (2009).Everything you ever wanted to know about statistics (well, sort of). In A. Field, Discovering Statistics Using SPSS (pp. 31-60). Thousand Oaks, CA: SAGE Publications Ltd.

15. VARIABILITY  The spread of scores around the mean  Range-the difference between the larges value and smallest value in a data set  Fractiles divide data into two or more equal parts such as percentiles PRIVITERA CHAPTERS 1-4

16. POPULATION VARIANCE  Population variance-the measure of variability for the average squared distance that scores in a population deviate from the mean  Deviation-the difference of each score from its mean  Sum of squares-is the sum of the squared deviations of scores from their mean  Variance formula for population is sum of squares divided by total population  Population standard deviation is the square root of the variance  Measure of variability for the average distance that scores deviate from their mean PRIVITERA CHAPTERS 1-4

17. SAMPLE VARIANCE  Measures how dispersed scores are from their mean in a given sample  Variance formula for sample variance is sum of squares divided by sample population minus 1  Sample standard deviation is the square root of the sample variance  Measure of variability for the average distance that scores deviate from their mean PRIVITERA CHAPTERS 1-4

18. STANDARD DEVIATION  Within a normal distribution…  68% of all scores lie within one standard deviation of the mean  95% of all scores lie within two standard deviations of the mean  99.7% of all scores lie within three standard deviations of the mean PRIVITERA CHAPTERS 1-4

19. REFERENCES  Privitera, G.J. (2012). Introduction to Statistics. In G.J. Privitera, Statistics for the Behavioral Sciences (pp. 2-26). Thousand Oaks, CA: SAGE Publications Ltd.  Privitera, G.J. (2012)Summarizing Data: Tables, Graphs, and Distributions. In G.J. Privitera, Statistics for the Behavioral Sciences (pp. 27-66). Thousand Oaks, CA: SAGE Publications Ltd.  Privitera, G.J. (2012). Summarizing Data: Central Tendency. In G.J. Privitera, Statistics for the Behavioral Sciences (pp. 67-94). Thousand Oaks, CA: SAGE Publications Ltd.  Privitera, G.J. (2012). Summarizing Data: Variability. In G.J. Privitera, Statistics for the Behavioral Sciences (pp. 95-125). Thousand Oaks, CA: SAGE Publications Ltd. PRIVITERA CHAPTERS 1-4