AP Stats Chapter 4 Review

Simple Random Sampling

• All elements in the population have an equal chance of being selected.

Stratified Random Sampling

• The population is divided into several strata (with a common variable like sex). Random samples are taken from each stratum.

• Could do random assignment instead of that (most likely

• Reduced variability and bias

Cluster Sampling

• Population is divided into groups, and a random sample of these clusters is selected → one cluster will be the entire sample

• Each cluster should be representative of the population (ex: town)

  • Ex → Clusters in books, one page=one cluster, randint(1,400) → look at random page selected

Systematic Sampling

Individuals are selected systematically from a sampling frame but this only NON-BIAS IF there is no relationship between the order or the sampling frame and the variables of interest. *The starting point must be randomize* ex. if you have a list take every nth person from the list, start at random pt

Convenience Sample

• One that is most convenient (friend, person in hallway)

Population in a statistical survey

• Entire group of individuals about which we want information

Sample

• Part of the population for which we actually collect information. We use information from a sample to conclude the entire population.

Bias

• There is bias in the design of a statistical study if it systematically favors certain outcomes

• Non-response, voluntary, and undercoverage

Reduce or negate bias through sampling:

• Multistage, Cluster, Stratified, SRS, Systematic

Types of Bias

• Non-response, Voluntary, Under-coverage, Response

Non Response Bias

• Occurs when individuals will not or cannot respond

Response Bias

• Occurs when respondents' answers may be affected by external influences, such as the wording of the question or interviewer behavior

Under coverage

• Occurs when parts of the population are not allowed to respond

Voluntary (and Convenience Sample)

• Will result of sample for not represent population

Sampling Errors

• Comes from the act of choosing the sample. ex., under coverage, convenience, and voluntary

Non-sampling Errors

• Errors are from sources other than the sample ex. Response bias and nonresponse

Sampling Frame

• List from which the sample is actually chosen ex. phone surveys: sampling frame-people with phones, generalize find to sample frame

Sample size determines how well the population is represented by the sample NOT the FRACTION of the population sampled

you need a large enough sample to make inferences about the population size

Experimental Design MAIN IDEA

In an experiment, one or more treatments are imposed on the experimental units (things) or subjects (people). Each treatment is a combination of levels of the explanatory variables which we call factors.

Experimental Design

• refers to the choice of treatments and the manner in which the experimental units or subjects are assigned to the treatments.

The basic principles of the statistical design of experiments**

• Control, replication and randomization

CONTROL

refers to the steps taken to reduce the possibility of a lurking variable. Three control strategies are: control group, placebo and blinding.

Control group

a baseline group that receives NO TREATMENT or a NEUTRAL treatment. to assess the treatment effects, the experimenter compares results in the treatment group to results in the control group.

Placebo

Often, subjects respond differently after they receive a treatment even if the treatment is neutral. A neutral treatment that has no real effect on the dependent variable is called a PLACEBO, and a subject's positive response to a placebo is called a placebo effect. To control for a placebo effect, researchers often administer a neutral treatment to the control group (ex. sugar pill in drug research, the drug is effective only if the subjects who receive the drug have better outcomes than those with the sugar pill).

Blinding

the practice of not telling subjects whether they are receiving the placebo. in this way, subjects in the control and treatment groups experience the placebo effect equally. (types: single and double blinding, where experimenter does not know who received treatment vs. placebo)

RANDOMIZATION

• The practice of using chance methods (a random number generator or flipping a coin) to assign subjects to a treatment.

• Potential effects of lurking variables are distributed at chance levels across treatment conditions.

REPLICATION

refers to the practice of assigning each treatment to many experimental subjects. in general, the more subjects in each treatment condition, the lower the variability of the dependent measures. (ex. if we had two treatments, it's best to have people in each group for more accurate results)

Three types of Experimental Designs:

completely randomized design, randomized block design and matched pairs design

completely randomized design

• simplest experimental design in terms of data and convenience. With this design, subjects are randomly assigned to treatments. (ex. Treatment: placebo or vaccine), relies on randomization to control for the effects of extraneous variables.

randomization block design

• The experimenter divides subjects into subgroups called blocks, such that the variability within blocks is less than the variability between blocks.

  • ex., blocking on gender: assign half male pop to treatment one and half male pop to treatment two, repeat w female pop

matched pairs design

• Type of randomized block design. Used when the experiment has only 2 treatment conditions and the subjects can be grouped into pairs based on a variable.

• Each pair of subjects is randomly assigned to different treatments

Experimental units

• The smallest unit of the design

  • Ex → all the people in all samples combined

Factors/ experimental variables

• Induvial variable that the investgator independtly manipulates, controls to observe its effect on the dependent variable.

Well-designed experiment

• Control group

• Replication → large enough samples

• Random assignment → cause and effect (observation cannot do)

• Multiple treatment groups for comparison