Sample Size and Statistical Theory PDF

Sample Size and Statistical Theory what should be...

Sample Size and Statistical Theory what should be my sample size? Determining sample size · Adhoc methods > given - by experience > - budgetary constraints > - May be blared and non scientific · Statistical Methods > given by population parameters - > - intended level of accuracy > - scientific · AdNoc Methods - budget constraints decide whether the budget : allows for a sufficient sample How sample. large the can be given the constraint > - comparable studies : use references of sample sites used in similiar studies in the part > sample size guided by not of thumb sample would be large enough - : can use stratified procedures Can use disproportionate  ampling if one of the groups ofthe population is relatively small Factors sample size Impacting If we ame comparing measur bu z or more groups , ex , we with control group and multiple treatment groups We need to motemwenchogh. representation as If the population we are working with is neterogenes gathering however info can be cortly. and varie a lot from if the value of inform. ampte amput. ↳nighvawabfor ardeci to a Wewill need a He to accurate which For new nasimplication · to ene accurate new Hi small one and representative of the sample site would be arge the Reputation If we have budgetary constraint In order to achieve significant wenave to consider the Coat tatistical reults , it is important to of sampling respondents. define the level of confident we want This will dictate the cost to acrie If we want higher the. of the sample of confidence we need to sample large number respondents of Basic statistic Terminology Parameter: value that describes some aspect of the population > measured characteristics of the population - > lower - care greek letter notation Statistic : value that describes some aspect of the sample to inter the population value > measurer computed from the sample data - > English letter as - notation  size and value greek englion don't we greek letter b) not trying actual parameter or statitic. are just The observable characteristics Population "Parameters" Population mean - normally known > the - "average" measure sample our goal is to obtain values 43 pop mean > - = as close as possible bytaking a sample from the population Population variance > measure of dispersion how - , read out the data is from the population mean (M1 > the difference of each value - from the mean is squared and averaged to get population mean  Descriptive "Statistics" · measurer of the sample · Describe basic features ofthe data in a study · Provide simple summaries about the sample and measurer · together with simple graphic analysis , they form the basir ofquantitative analysis of data How to make "data" Usable > Frequency and probability distributions to characterize the benavior - of the data - Measures of central Tendency * mean ] quick idea gives us a of & median now data is distributed * mode - Mearner of Dispersion * Range * Mean absolute deviation * standarddeviation * variance Probability and Frequency Distribution Probability refers to the likelihood of certain event (A) of interest : happening Formula P(A) 1 = : outcomes in A = N # outcomes in sample (total) space  EX. once EX Probability Distribution Probability Distribution mathematical function that describes : the likelihood of obtaining the possible values that a random variable can assume - random variables can be discrete or continuous · value of 15 does not exist be it is not Possible  Measurer of central Tendency way you should care about central tendency ?. By analyzing the values of mean , median , mode you can anticipate whether the data is skewed and the direction highly of the skewness must normal 547 widny used immetric 554 model distribution 12345678 1234 1234S  Measures of Dispersion Obertoa sample ↳ A normaat * measures of dispersion provide read a b c information ofhow t * it values are far away from The mean , we can say in the data variability is high * if data is concentrated around The mean , variability is low mean = o - sd I data is concentrated in = middle closer to the mean - Ja = 1 5 less data is. concentrated around The mean and more data is around the fails. Height of bell curve decreased - sa= 2 even less data is around the mean and more data is located in the tails. Bell cure decreased in height  sample statistics - Example 1) sample mean * + 1 ) 2 2 +o + + 2) to O + + + = 2) sample variance (52) Step 1 : calculate all deviation over Sep 2: square deviation cone deviroe : (value of observation - mean(/n-1 so i so S = 1 6).. Mandard 3 Deviction Formula : Nol = 1 21. 4 Median. , Mode , Range Median : = 1 Mode = 1 Con) Range = + 2-1-2) 4 : /. negatively stewed So · using sampling techniques , sample the population infor the laues of Th population  Ch 15. PT2 Distribution of sample mean Distribution of refers to the getting probability of · a particular sample mean Xi , when you sample the population generally assumed to be · normally distributed Distributions of sample observation we use the sample to meanhe our vanables which become ouobs  Where does the normal distribution comefrom Distribution of sample mean * The distribution related to all the sample means we have calculated from each random sample is ~ what is referred to the distribution of the sample mean - normal /100 = ↓ 100 ex) of those 100 samples , 24 of them had a sample mean of 4  Standard Deviation of sample mean (x) · Also known as standard error I varies sample to · sample -D is a measure of the variability · of the around around the true population mean rample mean I Standard error (Se) is · a how precise a ramp It measure of estimate (in this caserampe mean x) compared to population mean Thus , SD ofI sampl mean) is the sany as se of sample mean of error for · samplewite has implications sample mean, The sampling error Implications of sample site (h) In data is more spread at data varier man, Observations and less concentrated observation around the mean meaning higher error m as sample site increaser the probability of being closer to the the value ofthe population a increaser , lowering the sample error  Interval Estimation Interval : refers to a range of values bounded by the minimum maximum and values expected for the estimate Populationone · · The percentages mean the number of times values and to be expected to be found within the interval associated with That area ex. blu-1 and the mean , 34 1 % chance to find. Valver bu this lange · diEr properties allows us to relate confidence then with The normal. intervos Defined bared on 5th ·  - confiance the ex 68 3%.. of the time , values will be found by > D - and + st offe mean ex. 95 1 %. Of the time value will be bro-15th and 25th & of the mean confidence level x e 99 7 % of the time. , value will be fund bu ed of the mean , tu -3 D and + 3 my consistence tall is 99 7 %. confidence level and signif Level. m the I · remaining acombined is M => A a= alpha = given · (l-a) it level confidence > 11- 90) = 10 - - sig He The confidence level is related to the level of certainty. and derive to have certain results confidence Interval * remember, we can't e. the pop mean (M) , but given sampt data rom popul. range of valuer within I can etimate a which population parameter , the mean , can be located with certain confidence Well. The conf * Hul will allow Lower. me to identify the and upper limit ofthe interval * With value I can create confid inter 9 Men by T and sampling error  Stan = 2 Score Table O * lookfurcom basedon knownat ① T , ↓ Past = 0. 975 Tz-score Quantifying sample site T AD Ex. Estimating sample site calculate in E own * When confidence level required increasersample site alo increaser * When the ampling error inc Then. sampl The wity decreases have * sample size to reduce large ener