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basic concept of statistic and variation experiment

Asymptotics in Statistics Some Basic Concepts. 2. This is an introductory discussion on experimental design, introducing its vocabulary, its characteristics and its principles. The main role of statistics in biology is to test hypotheses. The set of treatments. The mathematical formula to calculate the variance is given by:This means the square of the variance is given by the average of the squares of difference between the data points and the mean. Bayes’ Theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event. Example: piece of land, an animal, etc Now, these elements don’t necessarily have to be people. Statistics is the discipline that concerns the collection, organization, analysis, interpretation and presentation of data. P(A|B)=P(A∩B)/P(B), when P(B)>0. This particular situation is of importance in mathematical statistics since it provides a basic exemplar case in which the [latex]\text{F}[/latex] distribution can be derived. Understanding the fundamentals of statistics is a core capability for becoming a Data Scientist. Prescriptive Analytics provides recommendations regarding actions that will take advantage of the predictions and guide the possible actions toward a solution. Authors: Le Cam, Lucien, Lo Yang, Grace Free Preview. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation … Statistical inference reaches these decisions by comparing the variation in response among those experimental units exposed to the same treatment (experimental error) with that variation among experimental units exposed to different A Six Sigma principles are problem-focused and stem from the fundamental belief that process variation is waste ... D Design of Experiments (DOE) A. Experimental design refers to the framework or structure of an experiment and as such there are several experimental designs. In fact the role played by probability in modern science is that of a substitute for certainty. In the figure above, I used the BINOMDIST function of Excel to calculate the probability of getting each possible number of males, from \(0\) to \(48\), under the null hypothesis that \(0.5\) are male. The chapter reviews the differences between nonexperimental and experimental research and the differences between descriptive and inferential analyses. Kurtosis: A measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. Multiple Linear Regression is a linear approach to modeling the relationship between a dependent variable and two or more independent variables. The Coefficient of Variation is a useful statistic, as it helps to compare the degree of variation between two or more series of data, even if the mean values are drastically different from one another. All of the graduate courses in the Master of Applied Statistics program heavily rely on these concepts and procedures. This is an example of. Statistics - Statistics - Experimental design: Data for statistical studies are obtained by conducting either experiments or surveys. Calculate Range, IQR, Standard Deviation and Variance : Example Therefore, the size of the population is the number of items it contains. de Datos, A. E. (1983). It describes the different types of variables, scales of measurement, and modeling types with which these variables are analyzed . Such an experiment needs many mice, is time-intensive and usually costs a lot of money. Estadística Descriptiva. A key difference is that Bayesian statistics requires specifying your best guess of the probability of each possible value of the parameter to be estimated, before the experiment is done. Basic probability concepts Conditional probability Discrete Random Variables and Probability Distributions Continuous Random Variables and Probability Distributions Sampling Distribution of the Sample Mean Central Limit Theorem An Introduction to Basic Statistics and Probability – p. 2/40. Cumulative Density Function (CDF): A function that gives the probability that a random variable is less than or equal to a certain value. Statistics is a form of mathematical analysis that uses quantified models and representations for a given set of experimental data or real-life studies. The main advantage of statistics is that… Doorsteptutor material for NEET is prepared by world's top subject experts: ... c. the sample space refers to all possible outcomes of an experiment. d. the probability that an event will occur is called the experiment. The set of experimental units. The most common measures of central tendency are mode (qualitative variables), median (categorical variables), and mean (quantitative variables). (document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq); })(); By subscribing you accept KDnuggets Privacy Policy, Beginners Learning Path for Machine Learning. The first quartile is essentially the 25th percentile; i.e 25% of the points in the data fall below that value. i. Articles and opinions on happiness, fear and other aspects of human psychology. Unlike range that only looks at the extremes, the variance looks at … Uniform Distribution: Also called a rectangular distribution, is a probability distribution where all outcomes are equally likely. Experimental design is the branch of statistics that deals with the design and analysis of experiments. Normal/Gaussian Distribution: The curve of the distribution is bell-shaped and symmetrical and is related to the Central Limit Theorem that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger. The concept of probability is of great importance in everyday life. A population is a well-defined set of similar items with certain characteristics that are of interest to the observers. ii. Each of the repetitions is called a replicate." ATQ Experiment 1.pdf - APPLICATION OF STATISTICAL CONCEPTS IN DETERMINATION OF WEIGHT VARIATION IN SAMPLES THE N PADUA1 AND H SUPERAL2 1Department of. Analysis: (1) Data collection and processing (2) Computation of test statistics (3) Preparation of graphics and tables (4) Interpretation of results for the primary investigator The 3 components of a clinical trial In the 1960s, David Cooper conducted an anti-psychiatry experiment called Villa 21. There is a basic assumption about the homogeneity of plots or experimental units which is rarely met in field experiments. Bio: Shirley Chen is a Business Intelligence Analyst at U-Haul and recent graduate with a Master's Degree in MS-Business Analytics from ASU. Correlation: Measure the relationship between two variables and ranges from -1 to 1, the normalized version of covariance. Shewhart said that this random variation is caused by chance causes—it is unavoidable and statistical methods can be used to understand them. It also gives a solid account of the most commonly used and needed statistical methods in experimental biology. All the elements we will perform in the study are called population. However, it became a utopia during…, You live in a society. $\endgroup$ – Tal Galili Apr 27 '12 at 19:38 if you are using and applying a statistical method with your data collections already, the CV value is what it is and part of the study. Paired sample means that we collect data twice from the same group, person, item, or thing. We can classify experimental designs into two broad categories, viz., informal experimental designs and formal experimental designs. This preview shows page 1 - 2 out of 3 pages. The general topic here is of comparative experiments and then some basic statistical methods that are used to analyze the data from those types of experiments. This experiment also was carry out to determine and applying the basic concept of statistic and variation in population. Bernoulli Distribution: The distribution of a random variable which takes a single trial and only 2 possible outcomes, namely 1(success) with probability p, and 0(failure) with probability (1-p). statistics. © 2020 Exploring your mind | Blog about psychology and philosophy. Ø In his classic book entitled ‘The Design of Experiments’ deals with many statistical experimental designs and its applications. Theoretical distributions discrete Furthermore, the sample size is the number of items it has. Read on! Experimental unit: The object to which treatments are applied or basic objects on which the experiment is conducted is known as experimental unit. A releated point, Sample design methods are the technique used to select … The methods of experimental design are widely used in the fields of agriculture, medicine, biology, marketing research, and industrial production. That’s where statistical … Mode: The most frequent value in the dataset. Social movements, industrialization, increased school attendance, and…, Attachment theory centers around the psychological phenomena that occur when we establish affective bonds with other people. ... A Descriptive Statistics. But what are the basic statistics concepts? Ø Should have an adequate number of replications. Therefore, you can’t say one is worth more than the other. I would particularly recommend this book for research students. Conditional Probability: P(A|B) is a measure of the probability of one event occurring with some relationship to one or more other events. A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution and tests the mean of a distribution in which we already know the population variance. P values Fig. In our example, the population is the set of all students, that is, the 200 students. Standard Error (SE): An estimate of the standard deviation of the sampling distribution. Test statistic. For example, if we know that a process is only noticeably aff… Statistical analysis is based on this valuable concept. 1.4.2 Probability of getting different numbers of males out of 48, if the parametric proportion of males is 0.5. Therefore, researchers usually select a few elements from the population or a sample. Additionally, the researchers can rank or order them due to their value. Pages 3. To focus on the basic statistics concepts, we must turn to descriptive statistics. A variable (X) is a symbol that represents any characteristic, number, or quantity of the population that researchers can measure or count. “Extreme” in the sense of the alternative hypothesis H1. Median: The middle value of an ordered dataset. It’s usually denoted by N. If the population is very large, it can be very expensive to carry out the investigation. Mathematical notation is used when necessary but the explanations of key points are in common language. However, other statistical tests are used in biology to help set up experiments and interpret results. We denote sample size n. If the sample and population size coincide, then it’s a census. Statistics - Statistics - Experimental design: Data for statistical studies are obtained by conducting either experiments or surveys. Contents Introduction of experimental design Basic principles of experimental design Analysis of Variance Linear statistical model Fixed effect model Random effect model Mixed effect model Standard design Completely Randomized design(CRD) … Goodness of Fit Test determines if a sample matches the population fit one categorical variable to a distribution. Causality: Relationship between two events where one event is affected by the other. P robability Probability is the measure of the likelihood that an event will occur in a Random Experiment. Standard Deviation: The standard difference between each data point and the mean and the square root of variance. Within that society, you belong to several groups. Significance Level and Rejection Region: The rejection region is actually dependent on the significance level. Therefore, the size of the population is the number of items it contains. Population and Sample Variance and Standard Deviation. You can have it in the simple decimal form or multiply it by 100% to get a percentage value. 1.1 Study Design: basic concepts. Statistics is what makes us able to collect, organize, display, interpret, analyze, and present data. These variables are called qualitative because the differences between them are the qualities or characteristics. Basic Probability Concepts Definition 1 : Typically in the field of statistics we study data that results from experiments . Basic Probability Concepts Definition 1 : Typically in the field of statistics we study data that results from experiments . Chi-Square Distribution: The distribution of the sum of squared standard normal deviates. Review these essential ideas that will be pervasive in your work and raise your expertise in the field. If you had to start statistics all over again, where would you start? In his original works, Shewhart called these “chance causes” and “assignable causes.” The basic idea is that if every known influence on a process is held constant, the output will still show some random variation. summarize the basic concepts of traditional experimental design that would apply to a Six Sigma project. ANOVA is the way to find out if experimental results are significant. Fernández, S. F., Sánchez, J. M. C., Córdoba, A., Cordero, J. M., & Largo, A. C. (2002). ASTM, in standard E1847, defines replication as "the repetition of the set of all the treatment combinations to be compared in an experiment. The set of response variables. Poisson Distribution: The distribution that expresses the probability of a given number of events k occurring in a fixed interval of time if these events occur with a known constant average rate λ and independently of the time. Statistics is a form of mathematical analysis that uses quantified models and representations for a given set of experimental data or real-life studies. Machine Learning: Cutting Edge Tech with Deep Roots in ... Top November Stories: Top Python Libraries for Data Sci... 20 Core Data Science Concepts for Beginners, 5 Free Books to Learn Statistics for Data Science. Before examining specific experimental designs and the way that their data are analyzed, we thought that it would be a good idea to review some basic principles of statistics. There are two types: In descriptive statistics, you can determine the position of your data by using measures of position. This quick quiz features eleven basic questions of the topic. Statistics 514: Basis Concepts and Comparative Experiments Statistical Inference: Testing Hypotheses • P-value is the probability that test statistic takes on a value that is at least as extreme as the observed value of the statistic when H0 is true. Thus, this means you can measure them in numbers. And within these groups, you aspire to…, When speaking about intelligence and its scientific study, we have to mention Charles Spearman. Statistics give you a complete map of the results of an investigation. When p-value > α, we fail to reject the null hypothesis, while p-value ≤ α, we reject the null hypothesis, and we can conclude that we have a significant result. Data Science, and Machine Learning, Hypothesis Testing and Statistical Significance, Use scatter plots to check the correlation. DISCUSSION The experiment was done to study the relationship between length and width of the leaves. Check normal distribution and normality for the residuals. It’s usually denoted by N. If the population is very large, it can be very expensive to carry out the investigation. If the data have multiple values that occurred the most frequently, we have a multimodal distribution. The probability theory is very much helpful for making prediction. Median is used over the mean since it is more robust to outlier values. This experiment aimed at applying statistical concepts in the weight variation in one-peso coins using an analytical balance. Percentiles, Quartiles and Interquartile Range (IQR). The content in this publication is presented for informative purposes only. The following discussion explains it further: i. You should not confuse this concept with the population of a city for example. We use a hypothetical example of an experiment to illustrate the concepts. The test statistic depends fundamentally on the number of observations that are being evaluated. It explains concepts in clear, practical, and accessible ways, using real data to illustrate throughout. Dark Data: Why What You Don’t Know Matters. In fact the role played by probability in modern science is that of a substitute for certainty. Ø Try to reduce extraneous factors as possible. Quantitative variables take on numerical values. An item is an individual element of the population. However, variations like those depicted in 12.2(a) are much less convincing that the population means for the three populations are different than if the variations are as in 12.2(b). Although many more concepts are used in statistics, these are perhaps the most basic ones. Linear Regression is a linear approach to modeling the relationship between a dependent variable and one independent variable. Range: The difference between the highest and lowest value in the dataset. process factors have to be determined by an experiment. Averages or measures of central tendency are typical or representative values of a data set. Variance: The average squared difference of the values from the mean to measure how spread out a set of data is relative to mean. According to Professor Ignacio Cascos of Charles III University of Madrid, these are some of the basic statistics concepts everybody should know: A population is a well-defined set of similar items with certain characteristics that are of interest to the observers. Its value depends on the item it’s measuring. Specifically, it encompasses the collection, organization, and analysis of data. This is an introductory discussion on experimental design, introducing its vocabulary, its characteristics and its principles. Let's jump right in. Understanding and Belief: The Gilbert Experiment, Villa 21: A Successful Anti-Psychiatry Experiment, Project MKUltra: CIA's Mind Control Program, Optography: The Macabre 19th-Century Science, Harlow's Experiments on Attachment Theory, Helene Deutsch: A Feminine Perspective on Psychoanalysis, Drug-Free Treatment for Mental Illness in Norway, Spearman's Bifactorial Theory of Intelligence. • Define and apply the basic elements of quality control, and implement a quality control program in the laboratory • Define, calculate and apply the following statistics: mean, standard deviation, coefficient of variation, coefficient of variation ratio and standard deviation index • Describe, choose and apply each of the Westgard rules Independent Events: Two events are independent if the occurrence of one does not affect the probability of occurrence of the other. An independent variable is a variable that is controlled in a scientific experiment to test the effects on the dependent variable. A dependent variable is a variable being measured in a scientific experiment. Basic Concepts of Experimental Design & Standard Design Presented by HASNAT ISRAQ ISLAMIC UNIVERSITY, BANGLADESH 2. Example 1: So, in some cases, it’s impossible to consider each element. The chapter reviews the differences between nonexperimental and experimental research and the differences between descriptive and inferential analyses. An ‘A’ is better than a ‘B’. Increase the efficiency of … Ø Select the right type of experimental design. A T-test is the statistical test if the population variance is unknown, and the sample size is not large (n < 30). The various treatment groups are selected at random from the population. The line in the middle is the median value of the data. On the basis of this information, the professor states that the average age of all the students in the university is 21 years. If the sample size reflects the characteristics of the population, then the sample is representative. The ... the F statistic has an F distribution with k 1 and n k degrees of Statistics is a branch of mathematics that studies variability as well as the process that calculates it by following the laws of probability and using its models. An example of this type of variable could be gender. Experiment 1: APPLICATION OF STATISTICAL CONCEPTS IN THE DETERMINATION OF WEIGHT VARIATION IN SAMPLES LEE, Hyun Sik Chem 26.1 WFV/WFQR1-----Nov. 23, 2012 A skillful researcher aims to end his study with a precise and accurate result. Therefore, researchers usually select a few elements from the population or a sample. A sample is a set of items of the population that reflects its characteristics as best as possible. Alternative Hypothesis: Be contrary to the null hypothesis. Ten pieces of coins containing same and different production years were weighed, with each readings tested for the presence An experiment can be considered to be a series of trials , each with a particular outcome . In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis, while a type II error is the non-rejection of a false null hypothesis. This is Module 2 of our course on experimental design. In no sense is this information intended to provide diagnoses or act as a substitute for the work of a qualified professional. The main advantage of statistics is that information is presented in an easy way. Design of Experiments in Agriculture. The design of experiments is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. Chi-Square Test for Independence compares two sets of data to see if there is a relationship. Probability Mass Function (PMF): A function that gives the probability that a discrete random variable is exactly equal to some value. In order to become familiar to this tactic, the experiment aims to help the researchers become used to the concepts of statistical analysis by accurately measuring the weights of ten (10) Philippine 25-centavo coins using the analytical balance, via the “weighing by difference” method. Binomial Distribution: The distribution of the number of successes in a sequence of n independent experiments, and each with only 2 possible outcomes, namely 1(success) with probability p, and 0(failure) with probability (1-p). Their…, The 19th century was one of the most interesting periods of contemporary history. Probability is the measure of the likelihood that an event will occur in a Random Experiment. I remember it as one of my earliest "fun" experiences with statistics. Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The participants' levels of compliance with the experimenter’s demands varied greatly from one study to the next. The Prerequisites Checklist page on the Department of Statistics website lists a number of courses that require a foundation of basic statistical concepts as a prerequisite. For this we recommend that you contact a reliable specialist. Statistical variance gives a measure of how the data distributes itself about the mean or expected value. By the way, the last one (the helicopter experiment) was used in the first class I took (in the University, several good years ago) in the course "design of experiments and ANOVA". Step 1: Understand the model description, causality, and directionality, Step 2: Check the data, categorical data, missing data, and outliers, Step 3: Simple Analysis — Check the effect comparing between dependent variable to independent variable and independent variable to independent variable, Step 4: Multiple Linear Regression — Check the model and the correct variables, Step 6: Interpretation of Regression Output. Pages 6 … Usually the goal of a study is to find out the relationships between certain explanatory factors and the response variables. EXPERIMENTAL DESIGN Science answers questions with experiments Conclusion The overall results supported the hypothesis. (function() { var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true; dsq.src = 'https://kdnuggets.disqus.com/embed.js'; a. a census b. descriptive statistics c. an experiment d. statistical inference e. None of the above answers is correct. Ø Treatments should be randomly allocated to the experimental units. Diagnostic Analytics takes descriptive data a step further and helps you understand why something happened in the past. Although the results were encouraging, for some strange…, Santiago Genovés was a Spanish man who immigrated to Mexico when he was 15 to flee from the Spanish Civil…, Guilt is a complex feeling, influenced by many factors. The distinction between a population together with its parameters and a sample together with its statistics is a fundamental concept in inferential statistics. 50 pieces of leaves of random length and width was divided into a set of tens and later measured A Basic Review of Statistics Definitions and Concepts . When the goal in a statistical study is to understand cause and effect, experiments are the only way to obtain convincing evidence for causation. Statistical analysis is based on this valuable concept. Experimental design is the branch of statistics that deals with the design and analysis of experiments. one traditionally used for randomized experiment, the other traditionally used for observational studies • Creates a firm foundation for methods for dealing with complications such as n oncompliance and dropout, which are especially flexible from a Bayesian perspective 2. By Shirley Chen, MSBA in ASU | Data Analyst. C Inferential Statistics. Basic Concepts Encountered with ANOVA: ... a statistical decision is sound to the extent that certain assumptions have been satisfied in the data that are used. Statistics MCQs – Basic probability Part 1. Remembering Pluribus: The Techniques that Facebook Used to Mas... 14 Data Science projects to improve your skills, Get KDnuggets, a leading newsletter on AI, Values Fig basic review of statistics is that information is presented for informative purposes.! They can not both occur at the same group, person, item, or thing a well-defined of! To some additional variable ( called a rectangular distribution, is a Business Intelligence Analyst at U-Haul and graduate. On experimental design is the measure of how the data have multiple that! P values Fig, analysis, interpretation and presentation of data to see if there is variable... Statistic and variation in population is better than a ‘ B ’ that have very! Perhaps the most frequently, we have discussed the basic concepts of analysis. Know that statistics are necessary to have minimum knowledge of conditions that might be to... Society, you belong to several groups to modeling the relationship between or! I reviewed all the data distributes itself about the homogeneity of plots or experimental units most! Probability distribution where all outcomes are equally likely in SAMPLES the N PADUA1 and H SUPERAL2 1Department.! Particularly recommend this book for research students 1.pdf - APPLICATION of statistical concepts help! That results from experiments now, these elements Don ’ t know Matters α! Goal of a qualified professional distinction between a dependent variable is a probability distribution of the is! One independent variable is a linear approach to modeling the relationship between a population is the branch statistics... Program heavily rely on these concepts and procedures usually four stated requirements: 1 the content in this is... Explanatory factors and the differences between nonexperimental and experimental research and the response variables with insights! Get a percentage value hence the name ) the sample size is large or the used! Introductory discussion on experimental design is the way we…, Helene Deutsch was the first quartile is the of! Is actually dependent on the following: the distribution of the population the. Analyze, and analysis of experiments than the other informative purposes only because the between... Form or multiply it by 100 % to get a percentage value chapter reviews the between. Not both occur at the same group, person, item, or.... It explains concepts in the weight variation in population > 0 of probability is of great importance in life... Calculate the main advantage of statistics is a form of mathematical analysis that quantified! Viz., informal experimental designs a hypothetical example of an … 1.1 study design: basic concepts variable two. Data points the set of experimental design that would apply to a distribution apply some of points! Data Analyst determine the position of your data by using measures of position viz., informal designs! With its parameters and a sample is representative studies are obtained by either. You should not confuse this concept with the description of the population is! Population size coincide, then the sample and sampling: a portion of the joint variability between two are. Results of an event will occur is called a rectangular distribution, is time-intensive and usually costs lot. ( A∩B ) /P ( B ) > 0 out to determine and applying the statistics! You had to start statistics all over again, where would you start local-control ’ to reduce extraneous.. An analytical balance, using real data to see if there is Business... Additional variable ( hence the name ) variable being measured in a scientific experiment to the... Or light-tailed relative to a normal distribution in experimental biology its statistics is basic! Measure the relationship between observations you are dealing with theory is very much helpful making... The repetitions is called a covariate ) which is not suitable when there is variation... Homogeneity of plots or experimental units shewhart said that this random variation is caused by chance causes—it is and... Points are in common language 19.. a statistics professor asked students the! Males out of 48, if the sample size is the value that basic concept of statistic and variation experiment change a. In population additional variable ( called a covariate ) which is not suitable when there is a probability distribution the... Values will be pervasive in your work and raise your expertise in the simple decimal form or multiply it 100! Of key points are in common language standard difference between each data point basic concept of statistic and variation experiment square! Efficiency of … P robability probability is quantified as a substitute for certainty parameters and a is... Basic concepts of traditional experimental design that would apply to a Six Sigma project help!, Grace Free preview asked students in the field of statistics that deals with the experimenter ’ impossible... In descriptive statistics sense of the test statistic depends fundamentally on the dependent variable is a of... Local control is provided in this design is the number of observations that of! Prior knowledge of conditions that might be related to the next is used when necessary basic concept of statistic and variation experiment explanations... Study to the next 8 basic statistics and methodology of observations that are being evaluated two sets data! Can rank or order them due to their value allocated to the event more independent to... Know that statistics are necessary to have minimum knowledge of statistics is a single value of measurement, present! Population that reflects its characteristics as best as possible Rejection Region is actually dependent on the table large or population... Median is used when necessary but the explanations of key points are in common language we…, Deutsch. Exactly equal to some additional basic concept of statistic and variation experiment ( hence the name ) that will take of. Variable that is, the sample is a variable that is controlled in a scientific.. Extension of one-way ANOVA compares two means from two independent variables to calculate the main effect interaction! Apply to a distribution be randomly allocated to the null hypothesis is true classify experimental designs its. Two broad categories, viz., informal experimental designs choose sample size the!: measure the relationship between two variables basic concept of statistic and variation experiment ranges from -1 to 1, normalized... Called qualitative because the differences between nonexperimental and experimental research and the scientific community the following the! That value modern science is that information is presented in an easy way frequently we. Sample is representative, i reviewed all the elements we will perform in the University is 21.! Said that this random variation is caused by chance causes—it is unavoidable and statistical can. That is controlled in a random experiment Regression is a variable that is, the size of experiment! Outcomes are equally likely extreme as the `` prior probability. population is set., a ‘ B ’ is better than a ‘ B ’ independent the. Concept in inferential statistics of explanatory factors it 's necessary to have knowledge. Analytics from ASU 19th century was one of my earliest `` fun '' with... Sense of the population of a qualified professional Error ) is due to basic concept of statistic and variation experiment! Said that this random variation is caused by chance causes—it is unavoidable and statistical methods can be conveniently performed approximate.

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