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This 3 page Class Notes was uploaded by Heli Patel on Saturday June 11, 2016. The Class Notes belongs to 3339 at University of Houston taught by Prof. C Poliak in Summer 2016. Since its upload, it has received 9 views. For similar materials see Statistics for the Sciences in Math at University of Houston.
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Date Created: 06/11/16
● Data ○ The facts and figures collected,analyzed, and summarized for presentation and interpretation. ○ cases are the objects described by a set of data. ○ label is a special variable used in some data sets to distinguish the different cases. ○ variable is any characteristic of an individual or object. ■ Categorical variable (factor)a case into one of several groups or categories ■ Quantitative variable numerical values ● Discrete countable set of values ● Continuous values within some interval ● Types of data ○ Population Data consists of all possible values pertaining to a certain set of observations or an investigation. ■ Experimentsstudy in order to observe the response, experiments can give good evidence for the factor(s) causing the response. ● Experimental units are the individuals on which the experiment is done. When the units are people, they are called subjects. ● treatment is the specific experimental condition applied to the units. I ● Factors are the explanatory variables in an experiment. Note that factors may have several levels. ● placebo is a dummy treatment that can have no physical effect. When the subjects respond to a placebo treatment,placebo effect. ■ Random Experiments ● we desire each replications of the experiment to be independent,the outcomes of some replications do not affect the outcomes of others. ● A random experiment has the following two characteristics: ○ 1. The experiment can be replicated an indefinite number of times under essentially the same experimental conditions. ○ 2. There is a degree of uncertainty in the outcome of the experiment. The outcome may vary from replication to replication even though experimental conditions are the same. ● sample space(Greek capital letter Ω (omega)) of a random experiment is the set of all possible outcomes. The sample space is determined by the desired outcomes. ○ Sample Data small section of the population taken for the purpose of investigation. ■ probability sample is a sample in which each member of the population has a known, nonzero chance of being selected for the sample ● Simple random sample (SRS) of size n consist of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. ● Stratified sampling subdivide the population into at least two different subgroups (strata) that share the same characteristics (as in gender or age bracket) then draw a simple random sample from each stratum. ● Cluster sampling divide the population area into sections (clusters), then randomly select some of the those clusters, and then choose all the members from those selected clusters. ● Systematic sampling selecting every kth member of the population for the sample. ● Resampling many samples are repeatedly taken from available points from the population. This technique is called the bootstrap. ■ Biased Sample systematically favors certain outcomes ● Voluntary Response Sample consists of people who choose themselves by responding to a general appeal. This type of sample is biased because people with strong opinions, especially negative opinions, are most likely to respond. ● Convenience Sampling chooses the individuals easiest to reach. ● Ways to obtain data ○ Previous information (Published Source) ○ Surveys ○ Designed Experiments ○ Observational Studies ● Describing Quantitative variable with numbers ○ Center mean, median or mode ○ Spread range, interquartile range, variance, or standard deviation ○ Location percentiles or standard scores ● Parameter and Satatistics ○ parameter is a number that describes the population. A parameter is a fixed number, but in practice we usually do not know its value. ○ statistic is a number that describes a sample. The value of a statistic is known when we have taken a sample, but it can change from sample to sample. We often use a statistic to estimate an unknown parameter. ○ The purpose of sampling or experimentation is usually to use statistics to make statements about unknown parameters, this is called statistical inference. ● Notattion of Parameter and Statistics ○ Name Statistic Parameter ○ mean xˉ µ mu ○ standard deviation s σ sigma ○ correlation r ρ rho ○ regression coefficient b β beta ○ proportion pˆ p
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