Intro to Statistics 1034 Ch 1 Notes.
Intro to Statistics 1034 Ch 1 Notes. Stat 1034
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This 7 page Class Notes was uploaded by Alyssa Notetaker on Monday February 1, 2016. The Class Notes belongs to Stat 1034 at University of Cincinnati taught by Sarah Myers in Spring 2016. Since its upload, it has received 65 views. For similar materials see Elementary Statistics I in Statistics at University of Cincinnati.
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Date Created: 02/01/16
Getting Started Ch1 Notes Material Extracted From Textbook (Brase, Charles Henry., and Corrinne Pellillo. Brase. Understandable Statistics: Concepts and Methods . 11th ed. N.p.: Cengage Learning, n.d. Print.) 1.1 Statistics: The study of how to collect, organize, analyze, and interpret numerical information from data. It is both the science of uncertainty and the technology of extracting information from data. ● Statistics helps people make decisions ● Statistics is a way to examine information ● Make inferences about populations by looking at samples ● The accuracy of a properly applied statistical procedure depends on the accuracy of the data (4). Data Individuals: are the people or objects included in the study. Variable: a characteristic of the individual to be measured or observed. Quantitative Variable: has a value or numerical measurement for which operations such as addition or averaging makes sense. Qualitative Variable: (Also called categorical variations) describes an individual by placing the individual into a category or group, such as male or female. “For instance, if we want to do a study about the people who had climbed Mt. Everest, then the individuals in the study are all people who have actually made it to the summit. One variable might be the height of the individuals (5). Other Variable Examples: Quantitative weight, age, income Qualitative gender, nationality Sources of Data Population Data: the data from every individual of interest. Sample Data: the data are from only some of the individuals of interest. Population Parameter: a numerical measure that describes an aspect of a population. Sample Statistic: is a numerical measure that describes an aspect of a sample. Data from a specific population are fixed and complete. Data from a sample has a higher chance of varying between samples. “For instance, if we have data from all other individuals who have climbed Mt. Everest, then we have population data. The proportion of males in the population of all climbers who have conquered Mt. Everest is an example of a parameter. On the other hand, if our data come from just some of the climbers, we have sample data. The proportion of male climbers in the sample is an example of a statistic… one of the important features of sample statistics is that they can vary from sample to sample, whereas population parameters are fixed for a given population” (5). ● Gathering sample data is often more realistic than population data. 4 Levels of Measurement: Nominal, Ordinal, Interval, Ratio ● Important because it helps indicate the type of arithmetic that is appropriate for data. ● Help indicate how to order data. Nominal Level: Applies to data that consists of names, labels, or categories. There are no implied criteria by which the data can be ordered from smallest to largest. Ordinal Level: Applies to data that can be arranged in order. However, differences between data values either cannot be determined or are meaningless. Interval Level: Applies to data that can be arranged in order in addition, differences between data values are meaningful. Ratio Level: Applies to data that can be arranged in order. In addition, both differences between data values are meaningful. Data at the ratio level have a true zero. True Zero/ Meaningful Zero: When zero means the absence of what it is trying to define. O degrees is not true zero because it still defines a temperature. 1.2 Random Samples ● Be wary of making hasty generalizations about a population about sample. Simple Random Sample: A simple random sample of n measurements from a population is a subset of the population selected in such a manner that every sample of size n from the population has an equal chance of being selected (13). ● Each member of a population has an equal chance of being selected. For a Simple Random Sample, every sample of the given size must also have an equal chance of being selected (13). Important Features of a Simple Random Sample 1. Every sample of specified size n from the population has an equal chance of being selected. 2. No researcher bias occurs in the items selected for the sample. 3. A random sample may not always reflect the diversity of the population of 10 cats and 10 dogs, a random sample of size 6 could consists of all cats. Easy Way to Get a Simple Random Sample ● Random number table ● Computer generator ○ Random selection does not mean haphazard selection. Procedure How to Draw a Simple Random Sample 1. Number all members of the population sequentially. 2. Use a table, calculator, or computer to select random numbers from the numbers assigned to the population members. 3. Create the sample by using population members with numbers corresponding to those randomly selected. Simulation: (Also called “Dry Lab Approach”) A numerical facsimile or representation of a realworld phenomenon also uses random number tables. Sampling Techniques Random Sampling: use a simple random sample from an entire population. Stratified Sampling: divide the entire population into distinct subgroups called strata. The strata are based on specific characteristics such as age, income, education level and so on. All members of a stratum share the specific characteristic. Draw random samples from each stratum (16). Strata: groups or classes inside a population that share a common characteristic. Population must be divided into at least 2 different strat. example men and women of population. Systematic Sampling : Number all members of a population sequentially. Then from a starting point select at random, include every kth member of the population in the sample (16). A group of people were standing in a line at a concert. You decide to select every 5th individual to include in a sample. Usually easy to acquire. Systematic sampling should not be used for populations that are repetitive or cyclical in nature (16, 17). Cluster Sampling: Divide the population into preexisting segments or clusters. The clusters are often geographic. Make a random selection of clusters. Include every member of each selected cluster in the sample (16). Conducting a survey of school children in a large city, we could first randomly select five schools and then include all the children from each selected school. Multistage Sampling: Use a variety of sampling methods to create successively smaller groups at each stage. The final sample consists of clusters. The government Current Population Survey interviews about 60,000 households across the United States each month by means of multistage sample design. For the Current Population Survey, the first stage consists of selecting samples of large geographic areas that do not cross state lines. These areas are further broken down into smaller blocks, which are stratified according to ethnic and other factors. Stratified Samples of blocks are taken. Finally, housing united in each chosen block are broken into clusters of nearby housing units. A random sample of these clusters of housing units is selected, and each household in the final cluster is interviewed. Convenience Sampling: Create a sample by using data from population members that are readily available. ● Does Run risk of being severely bias. Sampling Frame: the list of individuals from which a sample is actually selected. Undercoverage: When the sample frame does not match the population. ● Results from omitting population members from the sample frame. Sampling Error: The difference between measurements from a sample and corresponding measurements from the respective population. It is caused by the fact that the sample does not perfectly represent the population. Nonsampling Error: The result of poor sample design, sloppy data collections, faulty measuring instruments, bias in questionnaires, and so on. ● Sampling errors do not represent mistakes. They are simply the consequences of using samples instead of populations. However, be alert to nonsampling errors, which may sometimes occur inadvertently (18). 1.3 Introduction to Experimental Design Planning a Statistical Study Procedure Basic Guidelines for Planning a Statistical Study 1. Identify individuals or objects of interest. 2. Specify the variables as well as the protocols for taking measurements or making observation. 3. Determine if you will use an entire population or representative sample. If using a sample, decide on a viable sampling method. 4. In your data collection plan, address issues of ethics, subject confidentiality and privacy. If you are collecting data a business, store, college, or other institution, be sure to be courteous and to obtain permission as necessary. 5. Collect the data. 6. Use appropriate descriptive statistics methods and make decisions using appropriate inferential statistical methods. 7. Finally, note any concerns you might have about your data collection methods and list any recommendations for future studies. Census: Measurements or observations from the entire population are used. Sample: Measurements or observations from part of the population are used. Experiments and Observations Observational Study: Observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured. Experiment: A treatment is deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured. Placebo Effect: Occurs when a subject receives no treatment but (incorrectly) believes he or she is in fact receiving treatment and responds favorably. Completely Randomized Experiment ● One in which a random process is used to assign each individual to one of the treatments. ● Blocking is used to help control variables. Block: A group of individuals sharing some common features that might affect the treatment. Randomized Block Experiment: Individuals are first sorted into block, and then a random process is used to assign each individual in the block to one of the treatments. Control Group: This group receives a dummy treatment, enabling the researchers to control for the placebo effect. In general, a control group is used to account for the influence of other known or unknown variables that might be an underlying cause of a change in response in the experimental group. Replication of the experiment on many patients reduces the possibility that the differences in pain relief for the two groups occurred by chance alone. Double Blind Experiment: Neither the individuals in the study nor the observers know which subjects are receiving the treatment ● Control Bias Likert Scale: “Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree” type of survey. Potential Survey Pitfalls: Nonresponse: Individuals either cannot be contacted or refuse to participate. Nonresponse can result in significant undercoverage of a population. Truthfulness of Response: Respondents may lie intentionally or inadvertently. Faulty Recall: Respondents may not accurately remember when or whether an event took place. Hidden Bias: The question may be worded in such a way as to elicit a specific response. The order of questions might lead to biased responses. Also, the number of responses on a Likert Scale may for responses that do not reflect the respondent’s feelings or experience. Vague Wording: Words such as “often,” “seldom,” “and “occasionally” mean different things to different people. Interviewer Influence: Factors such as tone of voice, body language, dress, gender, authority, and ethnicity of the interviewer might influence responses. Voluntary Response: Individuals with strong feelings about a subject are more likely than others to respond. Such a study is interesting but not reflective of the population. Lurking Variables: One for which no data have been collected but that nevertheless has influence on other variables in the study. Confounding Variables: Two variables are confounded when the effects of one cannot be distinguished from the effects of the other. Confounding Variables may be part of the study, or they may be outside lurking variables.
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