10. co-effecient of variation. Biostatistics ppt
- 1. Coefficient of Variation and standard error of mean CHAPTER: MEASURES OF CENTRAL TENDENCY
- 2. What is coefficient of variation? The coefficient of variation (CV) is a measure of relative variability. It is the RATIO of the standard deviation to the mean (average) For example, the expression “The standard deviation is 15% of the mean” is a CV. If you are comparing the results from two tests that have different scoring mechanisms. If sample A has a CV of 12% and sample B has a CV of 25%, you would say that sample B has more variation, relative to its mean.
- 3. FORMULA Coefficient of Variation = (Standard Deviation / Mean) * 100.
- 4. Coefficient of Variation Example A researcher is comparing two multiple- choice tests with different conditions. In the first test, a typical multiple-choice test is administered. In the second test, alternative choices (i.e. incorrect answers) are randomly assigned to test takers. The results from the two tests are: Regular test Test 1 Rando mized answers Test 2 Mean 59.9 44.8 SD 10.2 12.7
- 5. Calculation using the formula CV=(SD/Mean)*100 Regular test Randomi zed answers Mean 59.9 44.8 SD 10.2 12.7 CV 17.03 28.35
- 6. Regular test: CV = 17.03 Randomized answers: CV = 28.35 The Coefficient of Variation should only be used to compare positive data on a RATIO SCALE. The CV has little or no meaning for measurements on an INTERVAL SCALE. Examples of interval scales include temperatures in Celsius or Fahrenheit, while the Kelvin scale is a ratio scale that starts at zero and cannot, by definition, take on a negative value (0 degrees Kelvin is the absence of heat).
- 7. Formula to calculate the CV by hand for a population or sample
- 8. Find coefficient of variation Example question: Two versions of a test are given to students. One test has pre-set answers and a second test has randomized answers. Find the coefficient of variation. Regular Test Randomize d Answers Mean 50.1 45.8 SD 11.2 12.9
- 9. Step 1: Divide the standard deviation by the mean for the first sample: 11.2 / 50.1 = 0.22355 Step 2: Multiply Step 1 by 100: 0.22355 * 100 = 22.355% Step 3: Divide the standard deviation by the mean for the second sample: 12.9 / 45.8 = 0.28166 Step 4: Multiply Step 3 by 100: 0.28166 * 100 = 28.266%
- 10. Standard error of mean The standard error (SE) of a statistic is the approximate standard deviation of a statistical sample population. The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. In statistics, a sample mean deviates from the actual mean of a population—this deviation is the standard error of the mean.
- 11. The standard deviation (SD) measures the amount of variability, or dispersion, from the individual data values to the mean, while the standard error of the mean (SEM) measures how far the sample mean of the data is likely to be from the true population mean. The SEM is always smaller than the SD. As the size of the sample data grows larger, the SEM decreases versus the SD; hence, as the sample size increases, the sample mean estimates the true mean of the population with greater precision.
Editor's Notes
- #6: Ratio scale- continuous and discrete quantitative numbers, In kelvin scale no measurement below 0- absolute zero.