Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
INTRO TO RESEARCH METHODS SPH-X590 SUMMER 2015 DATA ANALYSIS: METHODOLOGICAL BIG PICTURE STATISTICAL ANALYSIS PROBABILITY, INFERENCE & ESTIMATION NOTATION Presentation Outline • Review o o o o Structure of Research Dimensions of Research Research Process Study Designs • Statistical Analysis o Types of Statistics: Descriptive and Inferential o Notation The Structure of Research: Deduction The “Hourglass" Notion of Research Begin with broad questions narrow down, focus in. Operationalize OBSERVE Analyze Data Reach Conclusions Generalize back to Questions The Scientific Method Problem/Question Observation/Research Formulate a Hypothesis Experiment Collect and Analyze Results Conclusion Communicate the Results The Empirical Research Process: Step 1 Identification of Area of Study: Problem Formulation D E D U C T I O N T H E O R Y Step 2 Literature Review: Context Step 3 Research Objectives to Hypotheses: Content to Methodology • Concepts to Variables Step 4 Study Design I: Data Collection Methods • • Research Design: experimental, quasi-experimental, or non-experimental Time & Unit of Analysis Step 5 Procedures: Sampling, Assignment, Recruitment, & Ethics Step 6 Collection: Instruments, Materials, & Management Step 7 Study Design II: Analysis • • Statistical Approaches & Analytical Techniques Sample Size & Power Step 8 Results: Dissemination • Publication, Presentation, & New Application The Dimensions of Empirical Research: A movement from the theoretical to analytical Theories Analysis Data Collection Hypotheses Deductive Reasoning EMPIRICAL RESEARCH SCIENTIFIC METHOD Variables Constructs Propositions Concepts Measurement Postulates Data Analysis: In the Big Picture of Methodology Question to Answer Hypothesis to Test Theory Note: Results of empirical scientific studies always begin with the Descriptive Statistics, whether results conclude with Inferential Statistics depends of the Research Objectives/ Aims Study Design: Data Collection Method & Analysis Inferential Statistics Causal Inference Collect Data: Test Hypothesis, Conclusions, Interpretation, & Identification Relationships Measurements, Observations Data Storage Data Extraction Descriptive Statistics Describe Characteristics Organize, Summarize, & Condense the Numbers Decision: Statistics? Data Analysis: Types of Statistics • Descriptive Statistics o Summarization & Organization of variable values/scores for the sample • Inferential Statistics o Inferences made from the Sample Statistic to the Population Parameter. o Able to Estimate Causation or make Causal Inference • Isolate the effect of the Experimental (Independent) Variable on the Outcome (Dependent) Variable Data Analysis: Descriptive Statistics • Descriptive Statistics are procedures used for organizing and summarizing scores in a sample so that the researchers can describe or communicate the variables of interest. • Note: Descriptive Statistics apply only to the sample: says nothing about how accurately the data may reflect the reality in the population • Use Sample Statistics to “infer” something about relationships in the entire population: assumes sample is representative of population. • Descriptive Statistics summarize 1 variable: aka Univariate Statistics • Mean, Median, Mode, Range, Frequency Distribution, Variance and Standard Deviation are the Descriptive Statistics: Univariates Data Analysis: Inferential Statistics • Inferential Statistics are procedures designed to test the likelihood of finding the same results from one sample with another sample drawn from the same population: in fact, mathematically tests whether the sample results would be obtained if all possible samples from the population were tested. • Attempts to rule out chance as an explanation for the results: that results reflect real relationships that exist in the population and are not just random or only by chance. • Before you can describe or evaluate a relationship using statistics, you must design your study so that your research question can be addressed. • This is Methodology: where theory meets Data Collection Methods & Data Analysis. Data Analysis: Statistics Notation Capitalization In general, capital letters refer to population attributes (i.e., parameters); and lower-case letters refer to sample attributes (i.e., statistics). For example, • P refers to a population proportion; o and p, to a sample proportion. • X refers to a set of population elements; o and x, to a set of sample elements. • N refers to population size; o and n, to sample size. Greek vs. Roman Letters • Like capital letters, Greek letters refer to population attributes. • Their sample counterparts, however, are usually Roman letters. For example, • μ refers to a population mean; o and x, to a sample mean. • σ refers to the standard deviation of a population; o and s, to the standard deviation of a sample. Data Analysis: Statistics Notation Population Parameters By convention, specific symbols represent certain population parameters. Notation • μ refers to a population mean. • σ refers to the standard deviation of a population. • σ2 refers to the variance of a population. • P refers to the proportion of population elements that have a particular attribute. • Q refers to the proportion of population elements that do not have a particular attribute, so Q = 1 - P. • ρ is the population correlation coefficient, based on all of the elements from a population. • N is the number of elements in a population. Sample Statistics By convention, specific symbols represent certain sample statistics. Notation • x refers to a sample mean. • s refers to the standard deviation of a sample. • s2 refers to the variance of a sample. • p refers to the proportion of sample elements that have a particular attribute. • q refers to the proportion of sample elements that do not have a particular attribute, so q = 1 - p. • r is the sample correlation coefficient, based on all of the elements from a sample. • n is the number of elements in a sample. Data Analysis: Summation/ Sigma Notation Summation Notation is shorthand that relies on Greek alphabet and mathematical symbols to indicate how to process values: aka formulae. • = summation • X = Variable What do each of these mean? • X o Add up the values of X • X + 2 versus (X + 2) o Add up the values of X and add 2 to the Sum, o Add 2 to each value of X and then Sum the values • X2 versus (X)2 o Square each value of X and then Sum o Sum the values of X and then Square the Sum • (X + 2)2 versus (X2 + 2) o Add 2 to each value of X, square the value, then Sum the squared values o Square each value of X, add 2 to the value, then Sum the values Data Analysis: Summation/ Sigma Notation : summation X : Independent Variable, typically Y: Dependent Variable, typically N= Size of the Population n= Size of the Sample ≤ ≥ ≠ = : Equalities or Inequalities ± × ÷ + - : Mathematical Operators α: alpha, refers to constant/ intercept µ: mu, sample mean β: beta coefficient/ standardized δ: sigma, sample standard deviation δ2: sigma squared, sample variance