Chapter 3 Generating Data

Introduction to Data Collection/Analysis Exploratory Data Analysis: Plots and Measures that describe a set of measurements with no clear research questions posed. Statistical Inference: Methods used to make statements regarding population(s) based on sample data Statistical Design: Strategy to obtain data to answer research questions (gameplan) Anecdotal Evidence: Information obtained from individual, high profile, cases (plane crashes, storms, etc)

Data Sources Available Data: Information previously obtained and available in libraries and/or the Internet Sampling: Selecting a subset from population of interest and obtaining relevant information from individuals (observational study) Census: Information collected from all individuals in a population Experiment: Individuals are placed in various conditions by researchers and responses are then obtained

Experimental Design Experimental Units: Individuals participating in experiment (Humans often called Subjects or S s ) Treatment: Specific condition applied to units Factor: Explanatory variable used in experiment. Many experiments have more than 1 factor Factor Level: Value that a factor takes on. Example: Unplanned Purchases –68 subjects selected, response: #unplanned items purchased –Factors: Store Knowledge and Time Pressure –Factor Levels: Knowledge(Familiar/Unfamiliar) Time Pressure(Present/Absent) –Treatments: 4 Cominations of Knowledge and Time Pressure

Unplanned Purchases Experiment

Comparative Experiments Goal: Compare two or more conditions (treatments) Units assigned at random to receive 1 treatment (usually, although some designs have each unit receive each treatment) Placebo Effect: Phenomena where subjects show improvement even when given a dummy treatment Control Group: Subjects that receive a placebo or non-active agent or no treatment at all Biased Design: Favors certain response outcomes Randomization: Use of chance to assign units to treatment conditions

Principles of Experimental Design Control: Removing effects of lurking variables by comparing two or more treatments Randomization: Use of chance to allocate subjects to treatments. Removes personal biases. Makes use of tables/computer programs for random digits Replication: Apply treatments to as many units as possible Statistical Significance: Observed effect that exceeds what could be expected by chance

Miscellaneous Topics Blinding: Whenever possible, subject and observor should be unaware of which treatment was assigned. When neither knows it’s called “double-blind” Realism: Do the conditions in the experiment the real- world setting of interest to investigators Matching: Identifying pairs of units based on some criteria expected to be related to response, then randomly assigning one from each pair to each treatment Block Design: Extension of matching to more than 2 groups (subjects can be their own blocks and receive each treatment in some experiments)

Sampling Design Population: Entire set of individuals of interest to researcher Sample: Subset of population obtained for data collection/information gathering Voluntary Response Sample: Individuals who self-select themselves as respondents. Internet polls are example. Tend to be very biased. Simple Random Sample: Sample selected so that each group of n individuals is equally likely to be selected Probability Sample: Sample chosen by chance Stratified Random Sample: Simple Random samples selected from pre-specified groups (strata)

Miscellaneous Topics in Sampling Multistage Sampling: Government surveys tend to have multiple levels in the sampling process. Primary Sampling Unit Block Clusters of units Undercoverage: Groups in the population are not included in sample Nonresponse: Individuals Selected who do not respond Biases: –Response Bias: Subject gives answer to please interviewer –Recall Bias: Tendency for some subjects to remember something from past –Wording: Questions can be phrased to elicit certain responses

Introduction to Statistical Inference Parameter: Number describing a population Statistic: Number describing a sample Parameters are fixed (usually Unknown) values. Statistics vary from one sample to another due to different individuals

Sampling Distributions Sampling Distribution: Distribution of values that a statistic can take on across all samples from the population. –Shape: For large samples, the sampling distributions of sample means and proportions tend to be approximately normal –Center: The center of he sampling is equal to the parameter value in the population (unbiased) –Spread: The spread of the distribution decreases as the sample size increases (variability of statistic shrinks as sample size gets larger) –Margin of error: Bounds on the size of likely sampling error (difference between sample statistic and population parameter)