Data and Types of Data (Statistics and Probability)
- 1. Data and Data Collection Quantitative – Numbers, tests, counting, measuring Fundamentally--2 types of data Qualitative – Words, images, observations, conversations, photographs
- 2. Data Collection Techniques Observations, Tests, Surveys, Document analysis (the research literature)
- 3. Quantitative Methods Experiment: Research situation with at least one independent variable, which is manipulated by the researcher
- 4. Independent Variable: The variable in the study under consideration. The cause for the outcome for the study. Dependent Variable: The variable being affected by the independent variable. The effect of the study y = f(x) Which is which here?
- 5. Key Factors for High Quality Experimental Design Data should not be contaminated by poor measurement or errors in procedure. Eliminate confounding variables from study or minimize effects on variables. Representativeness: Does your sample represent the population you are studying? Must use random sample techniques.
- 6. What Makes a Good Quantitative Research Design? 4 Key Elements 1. Freedom from Bias 2. Freedom from Confounding 3. Control of Extraneous Variables 4. Statistical Precision to Test Hypothesis
- 7. Bias: When observations favor some individuals in the population over others. Confounding: When the effects of two or more variables cannot be separated. Extraneous Variables: Any variable that has an effect on the dependent variable. Need to identify and minimize these variables. e.g., Erosion potential as a function of clay content. rainfall intensity, vegetation & duration would be considered extraneous variables.
- 8. Precision versus accuracy "Precise" means sharply defined or measured. "Accurate" means truthful or correct.
- 9. Accurate Not precise Neither accurate nor precise Not accurate But precise Both Accurate and Precise
- 10. Interpreting Results of Experiments Goal of research is to draw conclusions. What did the study mean? What, if any, is the cause and effect of the outcome?
- 11. Introduction to Sampling Sampling is the problem of accurately acquiring the necessary data in order to form a representative view of the problem. This is much more difficult to do than is generally realized.
- 12. Overall Methodology: * State the objectives of the survey * Define the target population * Define the data to be collected * Define the variables to be determined * Define the required precision & accuracy * Define the measurement `instrument' * Define the sample size & sampling method, then select the sample
- 13. Sampling Distributions: When you form a sample you often show it by a plotted distribution known as a histogram . A histogram is the distribution of frequency of occurrence of a certain variable within a specified range. NOT A BAR GRAPH WHICH LOOKS VERY SIMILAR
- 16. Interpreting quantitative findings Descriptive Statistics : Mean, median, mode, frequencies Error analyses
- 17. Mean • In science the term mean is really the arithmetic mean • Given by the equation • X = 1 /n xi n i=1 Or more simply put, the sum of values divided by the number of values summed
- 18. Median • Consider the set • 1, 1, 2, 2, 3, 6, 7, 11, 11, 13, 14, 16, 19 – In this case there are 13 values so the median is the middle value, or (n+1) / 2 – (13+1) /2 = 7 • Consider the set • 1, 1, 2, 2, 3, 6, 7, 11, 11, 13, 14, 16 – In the second case, the mean of the two middle values is the median or (n+1) /2 (12 + 1) / 2 = 6.5 ~ (6+7) / 2 = 6.5 Or more simply put the mid value separating all values in the upper 1/2 of the values from those in the lower half of the values
- 19. Mode The most frequent value in a data set • Consider the set • 1, 1, 1, 1, 2, 2, 3, 6, 11, 11, 11, 13, 14, 16, 19 – In this case the mode is 1 because it is the most common value • There may be cases where there are more than one mode as in this case • Consider the set • 1, 1, 1, 1, 2, 2, 3, 6, 11, 11, 11, 11, 13, 14, 16, 19 – In this case there are two modes (bimodal) : 1 and 11 because both occur 4 times in the data set.