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Statistics- methodology in consideration of collecting, analyzing, interpre
Orangeburg Calhoun Technical College, SC has reference to this Academic Journal, Statistics- methodology in consideration of collecting, analyzing, interpreting in addition to drawing conclusions from collected dataAnastasia KadinaGM presentation 6/15/2015Design: Planning in addition to carrying out research studies;Description: Summarizing in addition to exploring data;Inference: Making predictions in addition to generalizing about phenomena represented by the data.Homer Simpson: Aw, you can come up alongside statistics so that prove anything, Kent. 14 percent of all people know that.Population – the collection of all individuals or items under consideration in a statistical study Sample – that part of the population from which information is collected Parameter ? statistical description of the populationPopulationSampleStatistical Data AnalysisVariable ? characteristic that varies from one item so that anotherQuantitative(numerical)Qualitative(categorical)DiscreteContinuous
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Observing the values of the variables yield dataObservation ? individual piece of dataData set/Data matrix ? collection of observations in consideration of variableData matrixk variables measured in sample alongside the size of nPresenting dataRelative frequency = Frequency / total # of observationsSample in addition to population distributions:Measures of center (averages)The mode: the value that occurs alongside the highest frequencyExample: 4, 2, 5, 2, 6, 1, 2: 2 occurs alongside a greatest frequencyIf greatest freq == 1: no modeCan be more than 1 mode2. The median: Arrange the observed values of variable in a data in increasing order.a. # of observations is odd: the value in the middle.b. # of observations is even: the number halfway between the two middle valuesExample: 2, 5, 7, 8, 9, 11: Median = 7.5 (len = 6)3. Sample mean: the sum of observed values in a data divided by the number of observations
Measures of variabilityRange: Range = max ? minStandard deviation: For a variable x, the sample standard deviation, denoted by sx or ?x (for sample), or ? (for population), is:SamplePopulationZ-Score (Standard score)How many standard deviations a value lies above or below the mean of the set of data;For normal distribution probability of the event (area under the curve) can be found in the tables by z.SamplePopulationEmpirical rule in consideration of symmetrical normal distribution:68% of the values lie within x ñ sx,95% of the values lie within x ñ 2sx,99.7% of the values lie within x ñ 3sx.Z-Score (Standard score)Z?: value of Z in consideration of which the area under the standard normal curve so that its right is equal so that ?.If we want so that take both ends of the distribution into account, we consider Z?/2
Neural Networks?. ?.The Undiscovered Country ? Jonathan Y. Clark Department of Computing University of Surrey firstname.lastname@example.org Conventional Programs Neural Networks Natural Neural Networks A Biological Neuron Perceptron Multilayer Perceptron Artificial Neural Networks Self-Organising Map (SOM) Lithops (Living Stones) Conclusions in addition to Summary That?s All Folks! (Bugs Bunny Copyright Warner Bros.)
Sampling of the populationRandom sample – a sample from a finite population random of it is chosen in such a way that each of the possible samples has the same probability of being selected.For random sample of size n of population N:Sampling distribution mean = population mean? = ?xStandard deviation (standard error of the mean):Infinite populationFinite populationStandard deviation correction factorCentral Limit TheoremFor large samples the sample distribution of the mean can be approximated closely alongside a normal distribution.Large: sample size n >= 30? = ?xZ? denotes the value of z in consideration of which the area under the standard normal curve so that its right is equal so that ?Z?/2 is such value that area under the standard normal curve between -Z?/2 in addition to +Z?/2 is equal so that 1 – ?? = ?xWhen we use ?x as an estimate of ?, the probability is 1 – ? that this estimate will be ?off? either way by at mostE = Z?/2 * (? / ?n) (standard error)Probability in addition to Confidence of StatementsIn general, we make probability statements about future values of random variables (e.g. potential error of an estimate) in addition to confidence statements once the data has been obtained.
Confidence intervalsFor large samples (n >= 30) in addition to ? is knownStudent?s t-testAlso good in consideration of small samples (< ? < X + t?/2* s / ?nt?/2 can be found in corresponding tables by df in addition to ?t-scoreError Bars- graphical representation of the variability of data in addition to are used on graphs so that indicate the error, or uncertainty in a reported measurementCommon Error Bars
Test of HypothesesA statistical hypothesis is an assertion about the parameter(s) of a population.Null hypothesis (H0) ? any hypothesis set up primarily so that see whether it can be rejected (is directly tested);Alternative hypothesis (HA) ? the hypothesis that we accept when the null hypothesis can be rejected.A significance test is a way of statistically testing a hypothesis by comparing the data so that values predicted by the hypothesis. Data that fall far from the predicted values provide evidence against the hypothesis.If the difference between what we expect in addition to what we observe is so small that it may well be attributed so that chance, the results are not statistically significant.The test statistics is a statistic calculated from the sample data so that test the null hypothesis. This statistic typically involves a point estimate of the parameter so that which the hypotheses refer.p-value- the probability, when H0 is true, of a test statistic value at least as contradictory so that H0 as the value actually observed. The smaller the p-value, the more strongly the data contradict H0. The primarily reported result of a significance test.The p-value summarizes the evidence in the data about the null hypothesis. A moderate so that large p-value means that the data are consistent alongside H0.Most studies require very small p-value, such as p 0.05, before concluding that the data sufficiently contradict H0 so that reject it. In such cases, results are said so that be significant at the 0.05 level. This means that if the null hypothesis were true, the chance of getting such extreme results as in the sample data would be no greater than 5%.
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