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 Statistics Science of Collecting/ interpreting data Population Study of complete set of people being studied population parameters Characteristics of the population sample subset of population from data are actually obtained samples Statistic Sample found by consolidating or summarizing the raw data Margin of Error describes range of values likly to contain the pop. parameter Sample stat- margin of error sampple stat+ margin of error Steps in Statisitcal study 1 identify goal 2 choose sample 3 collect data 4 use sample to make inferences 5 draw conclusions census collection of data from every population represtative data sample has relevent characteristics of the general population bias if..... tend to favor certain results Simple random sample sample item in such way that every sample of same size has equal chance of being selected Systematic sampling Simple system to choose sample..... 10th or every 50th Convenience sampling sample that happens to be convenient Cluster Sampling Divide pop into groups, then pick groups randomly stratified sampling use when concerned about differences amoung sub groups... draw random samples from the individual strata Subjects People or objects chosen from sample participant if subjects are people, called participants Observational Study Observe or measure characteristics of the subjects, but do not attempt to influence Experiment Apply some treatment and observe meta Analysis Study topic that has been the subject of many other studies Treatment group group which recieves the treatment being tested control group an experiment is the group of subjects who do not receive the treatment being tested Randomized Experiment Subjects are assinged to the treatment group or control group at random so that each has = chance of being assigned to either group. placebo effect lacks the active ingredient of a treatment being tested, identical in apperence to the treatment. placebo effect Situation which patients improve simply because thehy believe they are reciving a useful treatment single blind Do not know whether they are members of treatment group or members of control---- Experimenters know! double blind Niether participants nor any experimenters know who belongs to treatment or control case control Observational study- natually divides into two or more groups. *people who behave inder study form case * people who do not behave are controls selection bias Researchers select their sample in bias way participantion bias occurs anytime participation in a study is voluntary self selected survey people decide for themselves whether to be included in the survey Variable Item that can vary or take on different values Data Types Qualitative data Quantitative data Qualitative data Values that can be placed into nonumerical categories quantitative Values representing counts or measures continuous an take on any value in a given interval discrete can take on only particular values and not other values nominal level data that consist names, lables or catorgories.... Qualitiative and and can't be rank or ordered Ordinal level applies to qualitative data that can be arrange in some order( high to low) Interval level Qualititative data --- intervals are important Ratio level applies to Quantitative data-- intervals and ratios are important Random error Unpredictable events in the measurment process systematic errors Problem in measurment system Absolute error how far measured value lies from the true value Absolute= measured - true value Relative error measured value- true value ------------------------- x 100 true value accuracy how close a measurment approximates a true value Precision Amount of detail in a measurement Absolute Difference Absolute diff = compard - refernce val relative difference compard value- ref val --------------------- x100 Ref value Index numbers Index numbers= Value ------- x 100 ref val consumer price index Computed monthly, based on prices in a sample of more than 60,000 services Frequency tables 1. Categories 2. Frequency bin group catorgies relative frequency proportion or percentage of the data value that falls in category Relative Freq= Freq in categoriey ------------------- total freq Cumulative Freq number of data values in that category and all preceding categories Distribution way values are spread over all possiable values bar gragh bars representing freq dotplot dots represent freq pareto chart Bars arranged in freq order( nominal level) histogram bar graph--- which show distributions for quanitiative data stem leaf plot Histogram turned sideways.. no bars.. see indivdual data line chart distrobutions of quantitative data as a series of dots onnected by lines Mean Average value median middle value mode Most common value outlier data set which is much higher or much lower than mos values weighted mean sumof (each data value x its weight) ------------------------------------- sum of all weights A distribution is Symmetric if left half is a mirror image of its right Left Skewed Value are more spread out n the left side right skewed values are more spread out to the right side varation how widly spread out about the center of data set lower Quartile divides lower fouth from upper fouth Middle Quartile Overall Median Upper Quartile divides lower fourths three- fourths from upper three fouths five number summary Distribution consists of the following 1 lower value 2 lower value 3 median 4 upper Quartil 5 high quartil nth percentil Divides the bottom % of data values from the top (100-n)% Percentile of data value= number of values lessthat this data value -------------------------------- Total number of values in data set X 100 normal distribution symmetric, bell shaped distribution with single peak Relative Freq and Normal Distribution area under normal distribution curve corresonding to the range of vales on the horizontal axis is relative frequency of those values Total relative freq must be 1. area under the normal distribution curve must equal 1 condition for normal distribution 1.data values clustered near mean= single peaked 2.Values spread evenly around mean making symmetric 3.Large deviation from mean becomes incresingly rare= producing tapering tails 4.Indiviual data results from comnination of many different factors such as genetic and enviormental factors 68% Data falls within 1 Standard Deveiation of the mean 95% Data points fall within 2 standard deviation of the mean 99.7% Fall within 3 standard deviation of the mean Standard scores data values that lies above or below the mean z= standard score= data value-mean ---------------- Standard Deviation