# STATISTICAL METHODS PDF

Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation).Data collection · Terminology and theory of · Misuse · History of statistical science. STATISTICAL METHODSIn the s, the introduction, acceptance, and application of multivariate statistical methods transformed quantitative sociological. Statistical methods are mathematical formulas, models, and techniques that are used in statistical analysis of raw research data. The application of statistical methods extracts information from research data and provides different ways to assess the robustness of research outputs.

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It turned out that productivity indeed improved under the experimental conditions.

However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindness.

The Hawthorne effect refers to finding that an outcome in this case, worker productivity changed due to observation itself. Those in the Hawthorne study became more productive not because the lighting was changed but because they were being observed.

This type of study typically uses a survey to collect statistical methods about the area of interest and then performs statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps statistical methods a cohort studyand then look for the number of cases of lung cancer in each group.

Types of data[ edit ] Main articles: Statistical data type and Levels of measurement Various attempts have been made to produce a taxonomy of levels of measurement.

## Statistical methods in research.

The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any statistical methods transformation.

Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary as in the case with longitude and temperature measurements in Celsius or Fahrenheitand permit any linear transformation.

Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation.

### STATISTICAL METHODS

Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variableswhereas ratio and interval measurements are grouped together as quantitative variables statistical methods, which can be either discrete or continuousdue to their numerical nature.

Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data typepolytomous categorical variables with arbitrarily assigned integers in the integral data typeand continuous variables with the real data type involving statistical methods point computation.

But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being statistical methods. Other categorizations have been proposed.

For example, Mosteller and Tukey [18] distinguished grades, statistical methods, counted fractions, counts, amounts, and balances.

Nelder [19] described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman[20] van den Berg Whether or not a transformation is sensible to contemplate depends on the question one is trying to statistical methods Hand,p.

Methods of resampling, such as the bootstrap and the jackknife, allow practical solutions to previously intractable problems of statistical inference Efron and Tibshirani This is done by recomputing a test statistic perhaps 1, times, using artificially constructed data sets.

Computational algorithms for Bayesian analysis replace difficult or impossible algebraic derivations with computer-intensive simulation methods, such as the Markov chain algorithm, the Gibbs sampler, and the Metropolis algorithm Gelman et al. Related developments have occurred in the treatment of missing data, with applications of the EM algorithm and Markov chain Monte Carlo techniques Schafer The methods discussed above represent the major developments statistical methods statistical methods in sociology since the s.

With the rapid development of mathematical statistics and advances in computing, new methods have continued to appear.

Major advances have been made in the treatment of missing data Little and Rubin Developments statistical methods statistical graphics Cleveland are reflected in the increasing number of graphics appearing in sociological journals. Methods that require less restrictive distributional assumptions and are less sensitive to errors in the data being analyzed are now computationally feasible.

Robust methods have been developed that are insensitive to small departures from the underlying assumptions Rousseeuw and Leroy