Statistics contains many basic concepts including 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. Descriptive statistics can be used to summarize the population data. Numerical descriptors include mean and standard deviation for continuous data types (like income), while frequency and percentage are more useful in terms of describing categorical data (like education). To draw meaningful conclusions about the entire population, inferential statistics is needed. It uses patterns in the sample data to draw inferences about the population represented, accounting for randomness. Computational statistics, or statistical computing, is the interface between statistics and computer science. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics. Show
The statistical practice involves planning, summarizing, and interpreting uncertain observations. Because the purpose of statistics is to generate the best information from existing data, some authors consider statistics to be a branch of decision-making theory. Problem-solving and improvement methodologies such as six sigma use the statistical process approach in measure and analysis steps to finding out the process using experiments and samples. In a randomized experiment, the method of randomization specified in the experimental protocol guides the statistical analysis, which is usually specified also by the experimental protocol. For instance, Measurement System Analysis (MSA) is an experimental and mathematical method of determining how much the variation within the measurement process contributes to overall process variability. In this article, I want to introduce the most applicable and handy statistical concepts which would be helpful for launching a successful data science project. Mean or averageMean or average is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term “arithmetic mean” is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean and the harmonic mean. Variancevariance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of numbers are spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Standard deviationThe standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard 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. ErrorWorking from a null hypothesis, two basic forms of error are recognized: Type I errors where the null hypothesis is falsely rejected giving a “false positive”. Analysis of varianceANOVA is a form of statistical hypothesis testing heavily used in the analysis of experimental data. A test result (calculated from the null hypothesis and the sample) is called statistically significant if it is deemed unlikely to have occurred by chance, assuming the truth of the null hypothesis. A statistically significant result, when a probability (p-value) is less than a pre-specified threshold (significance level), justifies the rejection of the null hypothesis, but only if the a priori probability of the null hypothesis is not high. Chi-squared testA chi-square test, also written as χ2 test, is a statistical hypothesis test that is valid to perform when the test statistic is chi-square distributed under the null hypothesis, specifically Pearson’s chi-square test, and variants thereof. Pearson’s chi-square test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table. Correlation and dependenceCorrelation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. In the broadest sense correlation is any statistical association, though it commonly refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Pearson correlation coefficientPearson’s correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a “product moment”, that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name. Regression analysisRegression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables. The most common form of regression analysis is linear regression, in which a researcher finds the line that most closely fits the data according to a specific mathematical criterion. Spearman’s rank correlation coefficientThe Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson’s correlation assesses linear relationships, Spearman’s correlation assesses monotonic relationships (whether linear or not). If there are no repeated data values, a perfect Spearman correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other. Student’s t-testA t-test is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. When the scaling term is unknown and is replaced by an estimate based on the data, the test statistics follow a Student’s t distribution. The t-test can be used, for example, to determine if the means of two sets of data are significantly different from each other. Probability TheoryProbability theory is the study of possible events from a computational point of view. In other words, probability theory is a branch of mathematics that deals with the analysis of random events. A randomized test is an experiment in which all possible outcomes are known before the test is performed, but before the test is performed, it is not clear which result will occur and the test can be performed under the same conditions and at the desired frequency. The core of probability theory consists of random variables, random processes, and events. Probability theory, in addition to explaining random phenomena, examines phenomena that are not necessarily random, but by repeating the test many times, the results follow a specific pattern. The result of examining these patterns is the law of large numbers and the central limit theorem. Time series analysisTime series analysis comprises methods for analyzing time-series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. While regression analysis is often employed in such a way as to test theories that the current values of one or more independent time series affect the current value of another time series, this type of analysis of time series is not called “time series analysis”, which focuses on comparing values of a single time series or multiple dependent time series at different points in time. Interrupted time series analysis is the analysis of interventions on a single time series. In future articles, I will help you to find out more about other important concepts to have a piece of deep knowledge as the fundamental basics to be a professional data scientist. ReferencesRomijn, Jan-Willem (2014). “Philosophy of statistics”. Stanford Encyclopedia of Philosophy. Pekoz, Erol (2009). The Manager’s Guide to Statistics. Erol Pekoz. ISBN 9780979570438. Nikoletseas, M.M. (2014) “Statistics: Concepts and Examples.” ISBN 978–1500815684 Freedman, D.A. (2005) Statistical Models: Theory and Practice, Cambridge University Press. ISBN 978–0–521–67105–7 What statistical measure will be used if you are going to determine the most common?Mean (Arithmetic)
It is the value that is most common. You will notice, however, that the mean is not often one of the actual values that you have observed in your data set.
What measure of central tendency is generally used in determining the final grade of a student?Mean is generally considered the best measure of central tendency and the most frequently used one.
What are the statistical measures?There are three main measures of central tendency: the mode, the median and the mean. Each of these measures describes a different indication of the typical or central value in the distribution.
Which statistics that divides a set of scores in two equal numbers of scores?The median is the point in the distribution that splits the scores in two equal groups, which is also known as the midpoint of a distribution, or the 50th percentile. To calculate the median, organize the raw scores in rank order.
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