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Univariate Analysis
Univariate is a term commonly used in statistics to describe a type of data which consists of observations on only a single characteristic or attribute. A simple example of univariate data would be the salaries of workers in industry. Like all the other data, univariate data can be visualized using graphs, images or other analysis tools after the data is measured, collected, reported, and analyzed. Data types Some univariate data consists of numbers (such as the height of 65 inches or the weight of 100 pounds), while others are nonnumerical (such as eye colors of brown or blue). Generally, the terms categorical data, categorical univariate data and numerical data, numerical univariate data are used to distinguish between these types. Categorical univariate data Categorical univariate data consists of non-numerical observations that may be placed in categories. It includes labels or names used to identify an attribute of each element. Categorical univariate data usually use eith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Data
In statistics, a categorical variable (also called qualitative variable) is a variable (research), variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property. In computer science and some branches of mathematics, categorical variables are referred to as enumerations or enumerated types. Commonly (though not in this article), each of the possible values of a categorical variable is referred to as a level. The probability distribution associated with a random variable, random categorical variable is called a categorical distribution. Categorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data. More specifically, categorical data may derive from observations made of qualitative data that are summarised as counts or cros ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Descriptive Statistics
A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and analysing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics) by its aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent. This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory, and are frequently nonparametric statistics. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example, in papers reporting on human subjects, typically a table is included giving the overall sample size, sample sizes in important subgroups (e.g., for each treatmen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Level Of Measurement
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated in psychology and has since had a complex history, being adopted and extended in some disciplines and by some scholars, and criticized or rejected by others. Other classifications include those by Mosteller and Tukey, and by Chrisman. Stevens's typology Overview Stevens proposed his typology in a 1946 ''Science'' article titled "On the theory of scales of measurement". In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval", and "ratio", unifying both " qualitative" (which are described by his "nominal" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exploratory Data Analysis
In statistics, exploratory data analysis (EDA) is an approach of data analysis, analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell beyond the formal modeling and thereby contrasts with traditional hypothesis testing, in which a model is supposed to be selected before the data is seen. Exploratory data analysis has been promoted by John Tukey since 1970 to encourage statisticians to explore the data, and possibly formulate hypotheses that could lead to new data collection and experiments. EDA is different from Data analysis#Initial data analysis, initial data analysis (IDA), which focuses more narrowly on checking assumptions required for model fitting and hypothesis testing, and handling missing values and making transformations of variables as needed. EDA encompasses IDA. Overview Tukey defined data analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the ''tail'' is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value in skewness means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat. Thus, the judgement on the symmetry of a given distribution by using only its skewness is risky; the distribution shape must be taken into account. Introduction Consider the two d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range (statistics)
In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). It is expressed in the same units as the data. The range provides an indication of statistical dispersion. Closely related alternative measures are the Interdecile range and the Interquartile range. Range of continuous IID random variables For ''n'' independent and identically distributed continuous random variables ''X''1, ''X''2, ..., ''X''''n'' with the cumulative distribution function G(''x'') and a probability density function g(''x''), let T denote the range of them, that is, T= max(''X''1, ''X''2, ..., ''X''''n'')- min(''X''1, ''X''2, ..., ''X''''n''). Distribution The range, T, has the cumulative distribution function ::F(t)= n \int_^\infty g(x) (x+t)-G(x) \, \textx. Gumbel notes that the "beauty of this formula is com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Dispersion
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. Measures of statistical dispersion A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion. Examples of dispersion measures include: * Standard deviation * Interquartile ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Variability
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. Measures of statistical dispersion A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion. Examples of dispersion measures include: * Standard deviation * Interquartile r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outlier
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust statistics, robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode (statistics)
In statistics, the mode is the value that appears most often in a set of data values. If is a discrete random variable, the mode is the value at which the probability mass function takes its maximum value (i.e., ). In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population (statistics), population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions. The mode is not necessarily unique in a given discrete distribution since the probability mass function may take the same maximum value at several points , , etc. The most extreme case occurs in Uniform distribution (discrete), uniform distributions, where all values occur equally frequently. A mode of a continuous probability distribution is often conside ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
