• Differences Between Descriptive and Inferential Statistics

  Definitions of descriptive and inferential statistics are found in Section 1.1 of Weiss.  Basically, descriptive statistics is the study of ways to represent populations or samples graphically or numerically while inferential statistics deals with techniques used to make inferences about populations based on sample information.
  

• Population and Sample

Populations are well-defined collections of things, people, or objects that are of some interest and are studied in certain ways.  Some examples of populations are: (1) all full-time CSUS students enrolled at the end of the first week in spring semester 2001, (2) all residents of the greater Sacramento area (needs to be clearly defined) on November 6, 2000, (3) all sales amounts for January 30, 2001 at Macy's downtown Sacramento store, (4) all cars in CSUS parking lot 4 at 10 A.M. on January 30, 2001.  These are only a few examples--think of other examples of populations.  

Most populations consist of a large number of members.  For the examples shown above the size of population (1) is around 20,000, population (2) is about 1,900,000, population (3) is unknown but very large, and population (4( is probably between 500 and 1000.

Definitions are found in Weiss, Section 1.1.  You can use this to link to Internet web pages for the Weiss book.  The Chapter 1 button contains materials related to populations and samples.

• Sampling

  • Representative Samples

    In sampling from a population the goal is to obtain a representative sample, that is a sample representing all aspects of the population that are of interest.  For example, in determining the proportion of brown-eyed people in a population, the sample should have approximately the same proportions of blue-eyed, brown-eyed, and other-color-eyed people as the population.  Since these population proportions may not be known, it is rather difficult to devise a method that will produce a representative sample.
    
    

  • Simple Random Sampling

    As you will see later, a sufficiently large random sampling (or some variation of it) is likely to produce a representative sample.  At least, if done properly, random sampling will prevent a biased sample from being selected.  Sample size will be considered briefly later.

    Simple random sampling can be done with or without replacement.  In practice, sampling is usually done without replacement.  Assume that each element of a population can somehow be associated with a number from1 through the number of elements in the population.  If one of these numbers is selected, the associated element is to be included in the sample.  Then random sampling is equivalent to selecting numbers at random from the set of numbers associated with the population. 

    Use the random number table in your textbook or the random number table at this link to pick a random sample of size 6 from a population whose elements are numbered from 1 through 57.  Next pick a random sample of size 12 from a population whose elements are numbered from 1 through 342.

  • Systematic Sampling

    Systematic sampling is carried out by selecting a starting number at random and then selecting every kth number following the starting number.  The population elements associated with the selected numbers constitute the systematic sample.

  • Cluster Sampling

    A population is divided, perhaps naturally, into groups called clusters.  As an example, the population of students at CSUS is divided into classes chosen by the students.  Each class is considered a cluster.  In obtaining a simple random sample from this population, the person(s) doing the sampling might have to visit a number of classes to find the single (usually) person from each of those classes to be included in the sample.  As a time (and money) saving alternative, two or three classes (clusters) could be selected at random and all of the people in these classes would be considered to be the sample.  This is cluster sampling.  The clusters are selected at random and all of the elements in each of the selected clusters constitute the sample.
    
    

  • Stratified Random Sampling

    As in cluster sampling the population is divided into subgroups called strata.  For example, the students attending CSUS this semester are divided by gender (F or M), by class (Freshman, Sophomore, Junior, Senior, Graduate), by units (Full-Time or Part-Time), among others.  In selecting a sample of size 100 from this population, you might want your sample to reflect the percentages in the strata mentioned above.  If it is possible to find the percentages of students in each stratum, you could sample in such a way that your sample has approximately the same percentages.  At the beginning of a semester it is not known exactly what percentages of students fall into each of the categories noted above.  However, the percentages are probably fairly close to the percentages from last semester.  If, for example, the percentage of females was 55% and the percentage of males was 45% last semester, in selecting a sample of size 100, you might want 55 females and 45 males in your sample.  Simply take a simple random sample of size 55 from the current semester females and another random sample of size 45 from the males.  The combination of females and males is a stratified random sample.

  • Resources

Additional information, definitions, and examples of systematic, stratified, and cluster sampling are found in Sections 1.6 and 1.7 of Weiss.

An outstanding look at polling is found on the Gallup Organization website at this link.

• Experimental Design

  • Observational Studies
    

    In observational studies the statistician does not force some predefined structure on the collection of information.  A certain group is observed and statistics for that group are reported.

  • Designed Studies

    Designed studies are devised to extract the maximum amount of information from an experiment.  This may be necessary for reasons of cost, minimization of suffering of laboratory animals or human subjects, or danger.
    

    • Control

    • Randomization

    • Replication

  • Resources

    Materials on Experimental Design are found in Section 1.5 of Weiss.
    
    

• About Exam Questions

Examination questions will be of three types: (1) Work-out-the-answer questions--you will be presented with a situation where you must choose an appropriate statistical technique, use the technique to arrive at an answer, and possibly use the answer to answer a questions or questions that are posed in the question, (2) Short essays--you will be asked to write a paragraph or two describing a concept or, (2) True or False Questions.  In the Sample Exam Question section of each page, you will find two or three examples of examination questions from the section.