1. Chapter 11 Summarizing & Reporting Descriptive Data

2. Learning Objectives  Interpret descriptive data when summarized as measures of central tendency, variability, and correlation.  Use graphical presentations of descriptive data to understand research data.  Critique the appropriateness of statistics used to summarize descriptive data.  Select appropriate statistical techniques to summarize and present descriptive data.

3. How do readers benefit?  Gives reader a quick overview of the:  Sample subjects (specific)  Research variables  Conveys information using graphs/tables to enhance understanding  “Results” or “Findings” section

4. How do researchers benefit?  Check for coding errors  Visualize the descriptive data:  Shape of distributions  Determine if assumptions of statistical tests were met  Gain understanding of subjects and their responses  Gain understanding of data prior to inferential analysis

5. Statistical Techniques  Frequency Distribution  Central Tendency  Variability  Correlation

6. Levels of Measurement  Nominal  Categorical data / labels / no mathematical properties  Ordinal  Categorical data that are ranked  Interval  Data that are ranked with equal intervals  Ratio Data  Interval level data that have a true zero

7. Categorical DataContinuous Data NominalOrdinalIntervalRatio Low Med High Blue Green Red 1234512345 0123401234 Types of Data

8. A Frequency Table  Based on counts of each value of the data, not numerical calculations  Can be tabulated as simple counts or relative values (percentages)  Often represented graphically by a simple bar graph

9. Example of a Frequency Table Favorite Football Team FrequencyPercentage Southeastern2158.3% LSU719.4% Tulane513.9% Saints38.3% TOTAL36100.0%

10. Display of Frequency Data

11. The Histogram  Commonly used with interval and ratio data  Used to summarize data and represent the distribution of frequencies  Represents the shape of the data (normal vs. skewed)  Based on counts, not values

12. The Normal Distribution

13. Measures of Central Tendency  Summarize information about the average value of a variable  Mean: arithmetic average  Good summary measure, affected by extremes  Median: midpoint of a distribution of values  Stable measure, less affected by extremes  Mode: most frequently occurring value

14. Measures of Central Tendency: The Mean  The arithmetic average  Add all of the values and divide by the number of values  Can be disproportionately affected by outliers and extreme scores  Can be skewed

15. Measures of Central Tendency: The Median  The exact midpoint of the numbers of the data set  The value which has 50% of the data points above it and 50% of the data points below it  Generally used when you want to compare your performance to the performance of others  Less affected by extreme scores  Not often reported

16. Measures of Central Tendency: The Mode  The most frequently occurring value in the data set  The only measure of central tendency that can be applied to nominal data  Some data sets may not have a mode  Some data sets may have two or more modes (bi-modal; multi-modal)

17. Measures of Variability  Refers to the spread or variation of the data  Range: difference between highest (max) and lowest (min) values  Reflects only the extremes  Variance: value of the standard deviation squared  Standard deviation (SD): average distance from the mean of the values in the data set  Coefficient of variation (CV): depicts the SD relative to the mean

18. Measures of Variability  Standard Deviation  Calculated based on every value in the data set  Summarizes the average amount of deviation of values from the mean  Based on the concept of the bell curve

19. -3 -2 -1 0 +1 +2 +3  1 s = 68.2%  2 s = 95.4%  3 s = 99.8% A Normal Distribution

21. Measures of Variability  Coefficient of Variation  Comparison of the variability of different variables  Calculated by dividing SD by the mean (SD/Mean)  Interpretation of the CV  Large values (close to 1.0) reflect greater variation in the data set  Small values (close to zero) reflect less variation in the data set

22. Example of CV = (SD/Mean) Length of Stay MeanSDCV Pneumonia2.31.1.478 COPD4.53.4.756 Emphysema3.72.4.649 Asthma1.80.2.112

23. Measures of Relationship  Correlation analysis: examines the values of two variables in relation to each other  Depicts the strength and nature of the relationship between the two variables  Correlation coefficients:  Pearson product moment correlation  Spearman’s rank order correlation

24. Measures of Relationship  The correlation may be positive or negative  Value of 0 indicates no correlation  Values of -1 or +1 indicate perfect correlation  Observe for a linear relationship

25. Contingency Table  A two-dimensional frequency distribution in which the frequencies of two variables are cross-tabulated  Used with nominal and ordinal data  Considered relational

26. Example of a Contingency Table Gender WomenMenTotal Smoking Status N % Non-smoker 10 45.46 27.316 36.4 Light smoker8 36.4 16 36.4 Heavy smoker 4 18.28 36.412 27.3 Total22 100 44 100

27. Errors in Summarizing Data  Use of inappropriate statistics (Table 13.1)  Data entry errors  Not utilizing the entire data set  Over-interpreting the data results  Inconsistent representation of data

28. Use of Descriptive Data in Practice  Observe for trends in data  Apply descriptive data to nursing practice to enhance the practice  Aids in understanding disease processes in a specific patient population  Helps guides the development of an intervention study

29. Let’s see what you learned…