Introduction to Statistics

Randomization

a process of randomly assigning subjects to different treatment groups

Replication

repeating the essence of a research study, usually with different participants in different situations, to see whether the basic finding extends to other participants and circumstances

census data

systematically acquiring and recording information about the members of a given population Collect information from the full population. • Rarely practical

Name three methods for acquiring statistical information...

♦ Census ♦ Sampling ♦ Experimentation

What are the 3 basic principles of experimental design?

♦ Control ♦ Randomization ♦ Replication

In experimental design, what is a factor?

A factor is a variable whose effect on the response variable is of interest in the experiment. Ex: If we're watching for birth defects, maternal folic acid is a factor which can reduces spina bifida.

In experimental design, what is a level?

Levels are the possible values for a factor. Example: How much folic acid does the mother consume? This is a level.

Experimentation

Try out a new procedure, idea, or activity.

Describe Simple Random Sampling...

In simple random sampling, each possible sample of a given size is equally likely to be the one obtained.

What is a *population*?

In statistics, a population is the collection of all items (or people) under consideration in a statistical study.

control group

In an experiment, the group that is not exposed to the treatment; contrasts with the experimental group and serves as a comparison for evaluating the effect of the treatment.

control

In an experiment, the standard that is used for comparison

Describe a problem with Cluster Sampling...

Sometimes, the clusters can be more homogenous than the full population. Samples obtained by cluster sampling may not be representative of the population. Example: Cluster sampling of homes to determine average value of homes in a city. Since homes of similar value tend to cluster near one other, a single super-rich cluster could foul the sample.

Sampling

The process of selecting representative units from a total population • Collect information from a subset of the population

Describe the Procedure for *Stratified Random Sampling with Proportional Allocation*

♦ Divide the population into subpopulations (strata) ♦ From each stratum, obtain a simple random sample of size proportional to the size of the stratum. (Sample size for a stratum = total sample size * stratum size / population size). ♦ Use all members selected by step 2. Example: We have 2000 zebras. We want a sample size of 10. ♦ We divide them into 4 strata of sizes 400, 600, 800, and 200. ♦ From stratum ______, we take ______ zebras • From 400, we take 400*10/2000 = 2 zebras • From 600, we take 600*10/2000 = 3 zebras • from 800, we take 800*10/2000 = 4 zebras • from 200, we take 200*10/2000 = 1 zebra ♦ We use these zebras.

Describe the procedure for *Systematic Random Sampling*

♦ Divide the population size by the sample size and round down to the nearest whole number, m. ♦ Use a random number generator to get a random number, k, between 1 and m. ♦ Select for the sample those members of the population that are numbered k, k+m, k+2m, .... Example: We have a population of 100 students, and we number them from 1 to 100. We want to select 5 students at random. ♦ 100 / 5 = m = 20 ♦ We get the random number 18 so k = 18. ♦ We choose students 18, 18+20, 18+40, 18+60, and 18+80. These are students 18, 38, 58, 78, 98.

What is a *representative sample*?

A representative sample is a sample which closely reflects the relevant characteristics of the population under consideration.

In experimental design, what is a *response variable*?

A response variable is the characteristic of the experimental outcome that is to be measured or observed. Example: If we're watching for birth defects, the presence or absence of birth defects is the response variable.

What is an *observational study*?

An observational study is an assessment of data taken from real life. These studies do not include any controls. Example: A doctor finds 113 cases of prostate cancer among 22,000 men who had a vasectomy. This shows a 60% increased risk from the general population. Note: Observational studies can ONLY demonstrate correlation! Observational studies can NEVER demonstrate causation.

What is *descriptive statistics*?

Descriptive Statistics is the branch of statistics concerned with methods for organizing and summarizing information. Descriptive Statistics: ♦ Organizing information ♦ Summarizing information

What is a *designed experiment*?

Exactly what it sounds like. Researchers impose controls. Designed experiments CAN help establish causation.

What is a *sample*?

In statistics, a sample is the subset of the population from which information is obtained. Samples are usually taken because the full population cannot be assessed for practical reasons.

What is *inferential statistics*?

Inferential Statistics is the branch of statistics concerned with methods for drawing conclusions about a population by examining a *sample* of the population. Inferential Statistics is also concerned with measuring the reliability of such conclusions. Inferential Statistics ♦ Drawing conclusions from a sample of a population ♦ Measuring the reliability of conclusions drawn from samples.

What is *probability sampling*?

Probability sampling is a process by which samples are selected by probabilistic means. For example: Flipping a coin, or using a random number generator. Simple Random Sampling

Describe the Procedure for Cluster Sampling

♦ Divide the population into subgroups (clusters). ♦ Obtain a simple random sample of the clusters (Use random numbers to select a number of clusters) ♦ Use all the members of the clusters obtained in step 2 as the sample. Example: We have 300 students, we want to select a sample of 60 students. ♦ We divide them into clusters of 20 students. - Students in cluster 1 are students 1-20 - Students in cluster 2 are students 21-40 - There are 15 clusters total ♦ Since we want a sample of 60, and since each cluster contains 20 students, we need to randomly select 3 clusters. We use a random number generator to select clusters #3, #4, and #10. ♦ Our sample includes all students from these three clusters.