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Statistics, Data, and Statistical Thinking The Science of Statistics Statistics: The science of data.
Collection Evaluation Classification Summary Organization Analysis Interpretation Types of Statistical Applications Descriptive Statistics: Describe collected data. "86.8% of players participating in the Speed Training Program improved their sprint times." "2.6% of players participating in the Speed Training Program had decreased times." Types of Statistical Applications Inferential Statistics: Create generalizations about a group based on a subset (sample) of that group. "Participating in the Speed Training Program will improve your sprint time." Fundamental Elements of Statistics Experimental Unit: Object of interest. graduating senior Population: The set of units in which we are interested. all 1450 graduating seniors at WSU age (at graduation) Variable: Characteristic of an individual unit. Fundamental Elements of Statistics Sample: Subset of the population. Statistical Inference: Generalization about a population based on sample data. 100 graduating seniors at WSU Measure of reliability: Statement about the uncertainty associated with an inference. "The average age at graduation is 21.9 (based on sample of 100)..." "...0.5 years." Fundamental Elements of Statistics Elements of Descriptive Statistical Problems population/sample of interest investigative variables numerical summary tools (charts, graphs, tables) pattern identification in data Fundamental Elements of Statistics Elements of Inferential Statistical Problems population of interest investigative variables sample taken from population inference about population based on sample data reliability measure for the inference Types of Data Quantitative Data measured on a naturally occurring scale equal intervals along scale (allows for meaningful mathematical calculations) Types of Data Qualitative Data measured by classification only nonnumerical in nature Ordinal Data: Data whose categories can be meaningfully ordered (best to worst ranking, age categories). Nominal Data: Data whose categories do not have a meaningful order (political affiliation, industry classification, ethnic/cultural groups). Types of Data Different statistical techniques are used for quantitative vs. qualitative data. Qualitative and quantitative data can be used together in some techniques. Quantitative data can be transformed into qualitative data through category creation. Qualitative data cannot be meaningfully transformed into quantitative data. Collecting Data Data Sources published source designed experiment survey observational study Collecting Data Sampling Sampling is necessary if inferential statistics are to be used. Samples need to be representative. This is the most common sampling method to ensure the sample is representative. Random sampling ensures that each subset of fixed size is equally likely to be selected. Random Sampling Collecting Data A local TV station conducts exit polling during an election, selecting every 10th person who exits the polling station. Is this a random sample? No. Why? Before the first person is surveyed, there are only 10 subsets that can be selected from the whole population. Once the first person is surveyed, there is only 1 subset that can be selected from the whole population. The Role of Statistics in Critical Thinking Statistical literacy is necessary today to make informed decisions both at work and at home. Statistical thinking is required to critically assess data and the inferences drawn from it. Statistical thinking assists you in identifying research resulting from unethical statistical practices. The Role of Statistics in Critical Thinking Common Sources of Error in Survey Data Selection Bias: Exclusion of a subset of the population of interest prior to sampling. NonResponse Bias: Failure to receive responses from all sample members. Measurement Error: Inaccuracy in recorded data. Can be due to survey design, interviewer impact, or a transcription error. Summary Two (2) Types of Statistical Applications Six (6) Fundamental Elements of Statistics Descriptive Inferential experimental units population variable sample inference measure of reliability Summary Two (2) Types of Data
quantitative qualitative Four (4) Data Collection Methods
published source designed experiment survey observation Summary Three (3) Sources of Error in Survey Data
selection bias nonresponse bias measurement error ...
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- Fall '07