statistics

How to determine sample size in research     What should the sample size be, or how big or small should “n” be, is the most pressing question in sampling analysis. The objectives may not be met if the sample size (‘n’) is too small, and we risk significant expenses and resource waste if it is too large. One can generally state that the sample needs to be the ideal size, meaning it shouldn’t be either too big or too small. In theory, the sample size should be sufficiently large to provide a desired width confidence interval; therefore, the sample size must be determined logically before the sample is drawn from the universe. One must focus on the following points in mind: (1) Nature of universe: The universe may be either homogenous or heterogenous in nature. If the items of the universe are homogenous, a small sample can serve the purpose. But if the items are heteogenous, a large sample would be required. Technically, this can be termed the dispersion factor. (ii) Number of classes proposed: If many class groups (groups and sub-groups) are to be formed, a large sample would be required because a small sample might not be able to give a reasonable number of items in each class-group. (ii) Nature of study: If items are to be intensively and continuously studied, the sample should be small. For a general survey the size of the sample should be large, but a small sample is considered appropriate in technical surveys. (V) Accuracy standard and acceptable confidence level: We will need a comparatively larger sample if we want to maintain a high standard of accuracy or precision. The sample size must be increased fourfold in order to double the accuracy for a fixed significance level. (vi) Financial availability: In reality, the sample size is determined by the funds available for the research. This consideration should be made when choosing the sample size because larger samples raise the estimated cost of sampling. (vii) Additional factors to consider: unit type, population size, questionnaire size, and the availability of qualified researchers. Approaches to select sample size: There are two different methods for figuring out the sample size. The first method is used “to specify the precision of estimation desired and then to determine the sample size necessary to insure it” while the second method “uses Bayesian statistics to weigh the cost of additional information against the expected value of the additional information.” The first method is a commonly used method for figuring out ‘n’ because it can provide a mathematical solution. This technique’s drawback is that it fails to compare the expected value of information with the cost of information gathering. Although the second method is theoretically the best, it is rarely employed due to the challenge of determining the information’s value. First of all, it can be said that sampling error always occurs when a sample study is conducted, but it can be managed by choosing a sample that is large enough. The researcher must specify the level of precision he desires for his population parameter estimates. For instance, a researcher may like to estimate the mean of the universe within ±3 of the true mean with 95 percent confidence. In this case we will say that the desired precision is ±3. i.e., if the sample mean is Rs 100, the true value of the mean will be no less than Rs 97 and no more than Rs 103. In other words, all this means that the acceptable error, e, is 3. for different approaches and example: read the upcoming blog do you need the examples? https://tutorarif.com/

Population and Sample: Population Or Statistical Population: a population or a statistical population is a set or a collection of all Objects, and individuals or measurements or recordings,  Which may either be finite and or non finite, which has some relevance to some interest or some characteristics, the characteristic may be Heights, weights, ages, mases  number etc. the population is said to be of two types    (i) Real Population: real population is one whose individuals or recordings are unpredictable with out properly listing them, we need to first record them and know about the individuals For Example: (i)      Heights of college students since we will not be able to know about the heights of the students unless we record them one by one (ii)  Daily temperature      (ii)Hypothetical population: The population whose individuals are predictable even with out actually performing the experiment, or recording the individuals. For Example: (i)    A coin tossed since can predict the possible out comes even with out listing them so this is an hypothetical population.             Sample: A sample is any subset or any part of a population, the number of individuals and observation in the sample are known as sample size, which is denoted by small “n”        Parameter and Statistic: A parameter is any quantity or a value which is calculated from the whole population, a population mean,  a population variance are the examples of parameters While a Statistic is any value is calculated from the sample, with out considering the whole population. Observations and variable In Statistics the term Observations refers to some information, which are numerically recorded Or Observations are the recorded values of every element of a characteristic, for example:   Physical measurements(Weights and heights) On the other hand variable as name suggests refers to a characteristic which changes it values from individual to individual, place to place and time to time. For example:  height, weight, gender are variables and their values taken from different people are observations. Qualitative and Quantitative variables: Qualitative variable: A variable which can not  be expressed in numeric form. or a variable whose values or observations can not be numerically recorded.  qualitative variable is also know as an Attribute. For example:  Blood group, Colors of cars, gender of students etc. Quantitative Variable: Opposite to the qualitative variable we have a quantitative variable, Which refers to a variable which can be numerically expressed. For example: age of the students. income of families.        Discrete and  Continuous Variables: Discrete variable: discrete variable is a sub type of quantitative variable. It is a variable which can assume or take only discrete (non decimal) or a whole numbers. For example:  number of student in a class or a college Income of individuals Continuous variable: A variable which can assume any value fractional or integer in a give range or interval. For example: Age of the students temperature of a place Social Links:      

Origin Of the word Statistics: The Word “statistics” is said to have been derived either from Latin word “Status” the Italian word “Statista”, or German word “Statistik”  these all mean the same as  “Political State” or a Government. statistics was originally meant to state or government to know the population size, number of patients in hospitals, number of causalities and injured in any disaster. The roll of statistics was only limited to state holders and rulers and kings who needed to seek information about agricultural land, commerce, military potential, to estimate annual budget, impose tax according to annual expense. in 1602 Shakespeare used the word “Statist” is his drama named Hamlet. The census of the population and recording the trade and rates of the various commodities has been the tradition of the ancient human civilization. In ancient the Roman Empire was one of the first states to collect numerical information called the data. Now a days it is undeniable to accept that the availability of electronics computers is certainly a major factor in the modern development of statistics. And data plays very important role in all walk of life. Computer Technology provided many advantages over calculations by hand or by calculator, stimulated the growth of investigation into new techniques. In the time of Ancient Greece the Philosophers contribute Ideas-no quantitative analyses. In17th Century Jakob Bernoulli, Blais Pascal, Pierre de Fermate, Abraham De Moivre played a very vital role in  studying  affairs of state, vital statistics of populations  probability through games of chance, gambling. In 18th Century the Laplace and Gauss contributed much in regression analysis, correlation and probability distributions importantly in Normal distribution, normal Curve, in connection with the study of astronomy. In 19th Century statistical analysis, regression and corelatioin was first time used in Biology by Quetelet Galton (an astronomer) by studying the genetic variations In 20th century several statistician are active in developing new methods, theories and application of statistics. Pearson Gossett (Student) and Fisher studied natural selection using correlation, and formed first academic department of statistics, Biometrika journal, helped develop the Chi-Square analysis studied process of brewing, alerted the statistics community about problems with small sample sizes, developed Student’s test evolutionary biologists developed ANOVA, stressed the importance of experimental design. Name of some statisticians along with their introduction to different tests and techniques In 20th Century Wilcoxon a biochemist studied pesticides, non-parametric equivalent of two samples test. Kruskalis and Wallis the economists developed the non-parametric equivalent of the ANOVA. Spearman a psychologist developed non-parametric equivalent of the correlation coefficient. Kendall a statistician developed another nonparametric equivalent the correlation coefficient. www.youtube.com/@StatisticsandDataScience123 http://facebook.com/tutorarifsarangzai12 pk.linkedin.com/…/tutor-arif-saranagzai-1ab631323  

Meaning Of Statistics: Being a very vast subject different people think statistics differently how ever most of the people think of statistics in the following three ways: in General people consider statistics as a subjects which deals with averages, percentages, graphs, charts, and tables. Some other people think that statistics is a subject which consists of some methods, some rules, some techniques, and some formulae, which are used in collecting, and presentation of large amount of numerical information. While other people consider statistics to be a subject which is used to make inference about the population  on the basis of sample information.  it is interesting to note that inference is made either: (i) On the basis of sample information This is done when it is impossible or it costs much to consider the whole population. then we take a sample which is actually a part of the population and examine it, and then make some inference about the population, this is done in sampling techniques and estimation. (ii)  On the basis of past information: this is very effective that we collect past records and data use some technique like regression and others to estimate, and predict about the future outcome. these techniques are useful when there is dependency among the variables. Origin of Statistics: The word “Statistics” is said to be Either Latin root derived form “Status” of Italian word “Statista” these both mean the same as  political state or Government. Statistics originally  meant information useful to state or government. for example. the size of the population, the number of patient in the hospitals etc. Now a days The word statistics is defined in the following senses: (i ) Statistics in  Singular sense: in singular senses statistics means a subject which is a body of some methods, techniques, rules and formulae. which are useful in collection, presentation, analysis, and interpretation of Numerical facts or data. (ii)   Statistics in plural sense: In Plural Sense the word “statistics” refers to “numerical information” or numerical facts. for example: Statistics of prices   (data or information related to prices) Statistics of road accidents.   (data or information related to road accidents) statistics of educational institutions: Statistics in plural sense can also be called “Statistical Data”              https://tutorarif.com/the-difference-between-filers-and-non-filers/ http://linkedin.com/in/tutor-arif-saranagzai-1ab631323 are you interested in knowing history of statistics?  keep visiting the webite