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Week 1 day 1

by: Heli Patel

Week 1 day 1 3339

Heli Patel
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week 1 notes
Statistics for the Sciences
Prof. C Poliak
Class Notes
Stats, day1




Popular in Statistics for the Sciences

Popular in Math

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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