Data Collection Statistics 11/28 Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? LESSON Data Collection In research, statisticians use data in many different ways. Data can be used to describe situations. Data can be collected in a variety of ways, BUT if the sample data is not collected in an appropriate way, the data may be so completely useless that no amount of statistical torturing can salvage them.

Random Sampling Selected by using chance or random numbers Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Random Sampling Selected by using chance or random numbers Each individual subject (human or otherwise) has an equal chance of being selected Examples: Drawing names from a hat Random Numbers

Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Systematic Sampling Select a random starting point and then select every kth subject in the population Simple to use so it is used often

Convenience Sampling Use subjects that are easily accessible Examples: Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Convenience Sampling Use subjects that are easily accessible Examples: Using family members or students in a classroom Mall shoppers

Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Stratified Sampling Divide the population into at least two different groups with common characteristic(s), then draw SOME subjects from each group (group is called strata or stratum) Basically, randomly sample each subgroup or strata Results in a more representative sample

Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Cluster Sampling Divide the population into groups (called clusters), randomly select some of the groups, and then collect data from ALL members of the selected groups Used extensively by government and private research organizations Examples: Exit Polls

Types of Experiments Observational Studies Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Types of Experiments Observational Studies The researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations No interaction with subjects, usually No modifications on subjects Occur in natural settings, usually Can be expensive and time consuming Example: Surveys---telephone, mailed questionnaire, personal interview

More on Surveys Telephone Mailed Questionnaire Personal Interviews Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? More on Surveys Telephone Mailed Questionnaire Personal Interviews Less costly than personal interviews Cover a wider geographic area than telephone or pi Provides in-depth responses Subjects are more candid than if face to face Less expensive than telephone or pi Interviewers must be trained Challenge---some subjects do not have phone, will not answer when called, or hang up (refusal to participate) Subjects remain anonymous Most costly of three Tone of voice of interviewer may influence subjects’ responses Challenge –low number of subjects’ respond, inappropriate answers to questions, subjects have difficulty reading/understanding the questions Interviewer may be biased in his/her selection of subjects

Interaction with subject occurs, usually Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Experimental Studies The researcher manipulates one of the variables and tries to determine how the manipulation influences other variables Interaction with subject occurs, usually Modifications on subject occurs May occur in unnatural settings (labs or classrooms) Example: Clinical trials of new medications ,treatments, etc.

So once we’ve collected the data, what does it look like? Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? So once we’ve collected the data, what does it look like? A frequency distribution is symmetric when a vertical line can be drawn through the middle of a graph of the distribution and the resulting halves are approximately the mirror images. A frequency distribution is uniform (or rectangular) when all entries, or classes, in the distribution have equal frequencies. A uniform distribution is also symmetric. A frequency distribution is skewed if the “tail” of the graph elongates more to one side than to the other. A distribution is skewed left (negatively skewed) if its tail extends to the left. A distribution is skewed right (positively skewed) if its tail extends to the right.

Symmetric Distribution Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Symmetric Distribution 10 Annual Incomes 15,000 20,000 22,000 24,000 25,000 26,000 28,000 30,000 35,000 Income 5 4 3 2 1 f $25000 mean = median = mode = $ 25,000

Skewed Left Distribution Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Skewed Left Distribution 10 Annual Incomes 20,000 22,000 24,000 25,000 26,000 28,000 30,000 35,000 Outlier Income 5 4 3 2 1 f $25000 mean = $_______ median = $_______ mode = $________ 23,500 25,000 Mean ___ Median < 25,000

Skewed Right Distribution Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Skewed Right Distribution 10 Annual Incomes 15,000 20,000 22,000 24,000 25,000 26,000 28,000 30,000 1,000,000 Income 5 4 3 2 1 f $25000 121,500 mean = $_______ median = $_______ mode = $______ Mean ____ Median > 25,000 25,000

Summary of Shapes of Distributions Objective: Students will be able to identify 5 basic sample techniques, observational and an experimental study. Students will also explore mean, median, and mode. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you determine which sample to use? Summary of Shapes of Distributions Symmetric Uniform Mean = Median Skewed right Skewed left VERY IMPORTANT!!! Mean > Median Mean < Median

Homework: Poll 50 people (keep their ages) on whether they voted Republican (Donald Trump), Democratic (Hillary Clinton) or Libertarian (Gary Johnson) for the presidential election. Make a Google Sheet that includes: ID Number Age City of Residence Voter choice Answer the following questions in complete sentences: Explain how you completed your data collection. What data collection method did you use? Explain why you used that method.