Study Guide! Chapter 4 - Statistics and Probability

Section 1 - Sampling and Surveys

Terminology

• Population: entire group of individuals we want information about

• Census: collect data from every individual in the population

• Sample: subset of individuals in a population from which we actually collect data

• Individual: object described in a set of data → people, animals, things

• Bad Sampling

  • Convenience: choosing individuals from the population who are easy to reach results in a convenience sample. The design of a statistical study shows bias if it is very likely to underestimate or overestimate the value you want to know.

  • Voluntary Response Sampling: allows people to choose to be in the sample by responding to a general invitation.

• Good Sampling

  • Simple random sample: involves using a chance process to determine which members of a population are included in the sample

  • Stratified random sampling: selects a sample by choosing a simple random sample from each stratum and combining the simple random samples into one overall sample.

  • Cluster sampling → selects a sample by randomly choosing clusters and including each member of the selected clusters in the sample

  • Systematic: selects a sample from an ordered arrangement of the population by randomly selecting one of the first K individuals and choosing every Kth individual thereafter.

• Things that can go wrong when sampling

  • Non-response: occurs when an individual chosen for the sample can’t be contacted or refuses to participate

  • Response Bias: occurs when there is a systematic pattern of inaccurate answers to a survey question

  • Undercoverage: occurs when some members of the population are less likely to be chosen or cannot be chosen in a sample

Section 2 - Experiments

• Studies

  • Observational

    • Retrospective: Examines existing data for a sample of individuals

    • Prospective: Tracks individuals into the future

  • Experimental

    • Control Group: used to provide a baseline for comparing the effects of other treatments

    • Experimental Unit: object to which a treatment is randomly assigned

    • Subject: when the experimental unit is human

    • Treatment: specific condition applied to individuals in an experiment

    • Factor: variable that’s manipulated and may cause a change in the response variable

      • Levels: different values of a factor

    • Placebo: treatment that has no active ingredient, but is otherwise like other treatments

      • Placebo Effect: describes the fact that some subjects in an experiment will respond favorably to any treatment

  • Confounding Variables: two variables are associated when their effects on a response variable are the same

  • Double Blind vs Single Blind

    • Double blind: neither the subject or those who interact with and measure responses know which treatment the subject received

    • Single blind: either the subject or those who interact and measure the response don't know which subjects are getting which treatment

  • Replication: using enough experimental units to distinguish a difference in the effects of the treatments from chance variation due to the random assignment

  • Random Assignment: experimental units are assigned to treatments using a chance process

  • Randomized Block Design: in each block, experimental units are randomly assigned to treatments

    • Block: group of experimental units known BEFORE EXPERIMENT to be similar in some way that is expected to affect the response to the treatment

  • Matched Pairs: pairing, easy to compare

Section 3 - Using Studies Wisely

• Inference

  • Sampling Variability: refers to the fact that different random samples of the same size from the same population produce different estimates.  Estimates from larger samples are more precise opposed to smaller samples.

  • When the observed results of a study are too unusual to be explained by chance alone, the results are called Statistically Significant.

  • Proving causation

    • Experiment

      • Scope of Inference

        • Random individual selection

          • Allows inference about the population from which individuals were chosen

        • Random group assignment

          • Allows inference about the cause and effect

    • Study - there are criteria for establishing causation when you can’t perform an experiment; don’t just assume one thing causes another

      • Strong Association - check r

      • Consistent Association

      • Greater sample size, greater the correlation - larger values of explanatory variable = stronger responses

      • Cause precedes effect

      • Cause is plausible

  • Ethics: Don’t do bad stuff. Don’t experiment on real people, don’t traumatize babies, don’t kill people, Don’t do.

    • Confidential: All individual data must be kept confidential; only statistical group summaries can be made public

    • Consent: Subjects must give consent