Week 1: 8/31/15
Week 1: 8/31/15 MAT 121
Popular in Probability and Statistics for the Liberal Arts I
Popular in Mathematics (M)
This 4 page Class Notes was uploaded by Aria Sivick on Friday September 4, 2015. The Class Notes belongs to MAT 121 at Syracuse University taught by in Fall 2015. Since its upload, it has received 126 views. For similar materials see Probability and Statistics for the Liberal Arts I in Mathematics (M) at Syracuse University.
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Date Created: 09/04/15
RANDOM SAMPLE OF SIZE n SIMP TYPE Every individual in the group being sampled has the same chance of being on the sample LE RANDOM SAMPLE OF SIZE n Every group of n individuals has the same probably of being the sample S OF RANDOM SAMPLING Systematic Sampling we select some starting point and then select every kth Ex Every 50th element in the population Convenience Sampling we use the the results that are very easy to get Stratified Sampling we subdivide the population into at least two different subgroups or strata so that subjects within the same sub group share the same characteristics age brackets then we draw a sample from each subgroup or strata Cluster Sampling first divide the population area into sections or clusters then we randomly select some of this clusters and choose all members from those selected clusters A multistage sample design includes random stratified and clustered samp ling at different stages The end result is a complicated jumbling design less expensive than a normal random sampling Blind Subject is unaware of whether he received the treatment eg medicine vs placebo Double blind administrator of the treatment doesn t know which it is CONFOUNDING occurs in an experiment when the investigators are not able to distinguish among the effects of different factors 0 SAMPLING ERROR Occurs when the sampling has been selected randomly but there is a discrepency between a sample result and the true population result NONSAMPLING ERROR Result of human error including such factors as wrong data entries false data biased conclusions NONRANDOM SAMPLING ERORR Result of using a sampling method that isn t random such as convenience sample MAT 121 Descriptive Statistics conveying information Inferential Statistics AKA statistical inference Making an inference about a population based on what was observed in a sample POPULATION VS SAMPLE an entire group of interest subset of population at a manageable size Parameter a number that describes Statistic a number that describes a a population sample Population Proportion P Sample proportion P phat Population Mean M Sample Mean X xbar POTENTIAL PITFALLS Correlation does not imply causation 0 Ex A student will not do well on Test 2 simply because he did well on Test 1 PRECISE NUMBERS If a number is precise it does not mean that it is right A ROUNDING RULE Proportions and numbers between 0 and 1 when represented as decimals should be rounded to at least 3 decimal places 0 47 divide for a decimal 571 o 571 decimal moves two to the right for percent 571 5711000 O 831 8311000 o 259 two decimal places to the left 259 2591000 DATA L QUANTITATIVE VS numeric Typically from counts of measurements CATEGORAL qualitative attribute Typically from asking does a subject have an attributequot DISCRETE VS CONTINUOUS The possible values come from some interval of real numbers The possible values come from an infinite or countable set countable can be put in a list Typically from counting Typically measurements Ex Experiment Toss coin until HEADS observe number of tosses required 1 23 LEVELS OF MEASUREMENT Nominal Level of Measurement 0 gender hair color political affiliation nationality religion yes noundecidedquot Ordinal Level of Measurement 0 data can be arranged in order but differences either can t be determined or are meaningless Ex horrible bad mediocre good great rankings Interval Level of Measurement o Ordinal plus differences can be found and are meaningful There is no natural zero Ex Points in time temperature m Level of Measurement 0 Data can be absorbed differences exist and are meaningful There is a natural zero that being so ratios are meaningful Ex Almost all measurements lengths time durations Ex 14921066 14 OBSERVATIONAL STUDY VS EXPERIMENT No attempts to influence the data we apply a treatment and then try to observe its effects 1 Retrospective Study Case Study 0 Observation comes from the past 2 Cross Sectional Study 0 Comes from the present 3 Prospective Study Longitudinal 0 Data comes from the future
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