1 Important Terms Variable – A variable is any characteristic whose value may change from one individual to another A univariate data set consists of observations on a single variable made on individuals in a sample or population. A bivariate data set consists of observations on two variables made on individuals in a sample or population.

2 Type of Data Categorical Data  Example1: color: red, blue, green, white  Example2: gender: male, female  Example3: levels: high, middle, low Numerical Data  Discrete – if the possible values are isolated points on the number line. Example 4: the number of students: 42, 70, 240, 16  Continuous – if the set of possible values forms an entire interval on the number line. Example 5: the height of students: 6.52’, 6.28’, 5.12’,… Note: Even though the heights are only measured accurately to 1 hundredth of an feet, the actual height could be any value in some reasonable interval.

3 Planning and Conducting a Study  Understand the Nature of the Problem  Decide What to Measure and How to Measure It  Collect the Data  Summarize the Data & Perform a Preliminary Analysis  Do the Formal Data Analysis  Interpret the Results Steps of the Data Analysis Process

4 Observational Study: if the values of the variable(s) of a sample from one or more populations is observed.  Observational studies are usually used to draw conclusions about the population or about differences between two or more populations. Experimental study: if the values of one or more response variables are recorded when the investigator controls (or manipulates) one or more factors.  Experiments are usually used when attempting to determine the effect of the manipulation of the factors being controlled. Collection of Data

5 Observational Study Sample survey: a snapshot of the population based on a sample observed at a point in time.  Population/Sample (census) Prospective study: track changes in a population by following a sample forward in time. Retrospective study: track changes in a population by following a sample forward in time.  Comparative studies  Cohort study: follow a group of people to compare who develop disease.  Case-control study: identify a case group with disease and a control group without disease, then look back for risk factors.

6 Observational Study An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. -Difficult to measure or gauge the effect of an action or procedure -Lurking variables are uncontrolled so the study may be confounded +Can use available data

7 Sampling Methods A representative sample: a sample that does not differ in systematic and important ways from the population. Simple Random Sample (See srs.sas) Stratified Random Sample Multistage Cluster Sample Systematic Sample

8 Sampling Methods  A Simple Random Sample of size n is a sample that is selected in a way that ensures that every different possible sample of the desired size has the same chance of being selected.  A common method of selecting a random sample is to first create a list, called a sampling frame of the individuals in the population. Each item on the list can then be identified by a number, and a table random digits or a random number generator can be used to select the sample.

9 Selection Bias is the tendency for samples to differ from the corresponding population as a result of systematic exclusion of some part of the population. Measurement or Response Bias is the tendency for samples to differ from the corresponding population because the method of observation tends to produce values that differ from the true value. Nonresponse Bias is the tendency for samples to differ from the corresponding population because data is not obtained from all individuals selected for inclusion in the sample. Note: Bias is introduced by the way in which a sample is selected so that increasing the size of the sample does nothing to reduce the bias Types of Bias

10 Experimental Studies An experiment is a planned intervention undertaken to observe the effects of one or more explanatory variables, often called factors, on a response variable. Any particular combination of values for the explanatory variables is called an experimental condition or treatment.

11 Experimental Studies An experiment deliberately imposes some treatment on individuals in order to observe their responses. +Allows the measurement of effect of a treatment +Can help to control lurking variables +Can give good evidence of causation -May not measure realistic effects. Not necessarily workable in real life.

12 Principles of Experimental Design The fundamental principles of statistical design of experiments are: 1)Direct Control Holding extraneous factors constant so that their effects are not confounded with those of the experimental conditions. 2)Blocking Using extraneous factors to create groups (blocks) that are similar. All experimental conditions are then tried in each block. 3) Randomization Random assignment (of subjects to treatments or of treatments to trials) to ensure that the experiment does not systematically favor one experimental condition over another. 4) Replication Ensuring that there is an adequate number of observations in each experimental condition. 5) Repeat Measurements Measuring each experimental unit repeatedly to reduce measurement errors.

13 Basic Experimental Designs Completely Randomized Design All experimental units are assigned at random to the treatments. Randomized Block Design “Similar” experimental units are first grouped into blocks and then within each block the units are randomly assigned to the treatments. (See crd_rbd.sas)