Category: Big Data & Analytics

Statistics – Data collection – Observation ”; Previous Next Observation is a popular method of data collection in behavioral sciences. The power, observation has been summed by W.L. Prosser as follows “there is still no man that would not accept dog tracks in the mud against the sworn testimony of a hundred eye witnesses that no dog had passed by.” Observation refers to the monitoring and recording of behavioral and non behavioral activities and conditions in a systematic manner to obtain information about the phenomena of interest, ”Behavioral Observation” is: Non verbal analysis like body movement. eye movement. Linguistic analysis which includes observing sounds like ohs! and abs! Extra linguistic analysis which observes the pitch timbre, rate of speaking etc. Spatial analysis about how people relate to each other. The non behavioral observation is an analysis of records e.g. newspaper archives, physical condition analysis such as checking the quality of grains in gunny bags and process analysis which includes observing any process. Observation can be classified into various, categories. Type of Observation Structured Vs. Unstructured Observation – In structured observation the problem has been clearly defined, hence the behavior to be observed and the method by which it will be measured is specified beforehand in detail. This reduces the chances of observer introducing observer”s bias in research e.g. study of p1ant safety compliance can be observed in a structure manner. Unstructured analysis is used in situations where the problem has not been clearly defined hence it cannot be pre specified that what is to be observed. Hence a researcher monitors all relevant phenomena and a great deal of flexibility is allowed in terms of what they note and record e.g. the student”s behavior in a class would require monitoring their total behavior in the class environment. The data collected through unstructured analysis should be analyzed carefully so that no bias is introduced. Disguised Vs. Undisguised Observation – This classification has been done on the basis of whether the subjects should know that they are being observed or not. In disguised observation, the subjects are unaware of the facts that they are being observed. Their behavior is observed using hidden cameras, one way mirrors, or other devices. Since the subjects are unaware that they are being observed hence they behave in a natural way. The drawback is that it may take long hours of observation before the subjects display the phenomena of interest. Disguised observation may be: Direct observation when the behavior is observed by the researcher himself personally. Indirect observation which is the effect or the result of the behavior that is observed. In undisguised observation, the subjects are aware that they are being observed. In this type of observation, there is the fear that the subject might show a typical activity. The entry of observer may upset the subject, but for how long this disruption will exist cannot be said conclusively. Studies have shown that such descriptions are short-lived and the subjects soon resume normal behavior. Participant vs. Non-Participant Observation – If the observer participates in the situation while observing it is termed as participant observation. g. a researcher studying the life style of slum dwellers, following participant observation, will himself stay in slums. His role as an observer may be concealed or revealed. By becoming a part of the setting he is able to observe in an insightful manner. A problem that arises out of this method is that the observer may become sympathetic to the subjects and would have problem in viewing his research objectively. In case of non-participant observation, the observer remains outside the setting and does not involve himself or participate in the situation. Natural vs. Contrived Observation. – In natural observation the behavior is observed as it takes place in the actual setting e.g. the consumer preferences observed directly at Pizza Hut where consumers are ordering pizza. The advantage of this method is that the true results are obtained, but it is expensive and time consuming method. In contrived observation, the phenomena is observed in an artificial or simulated setting e.g. the consumers instead of being observed in a restaurant are made to order in a setting that looks like a restaurant but is not an actual one. This type of observation has the advantage of being over in a short time and recording of behavior is easily done. However, since the consumer”s are conscious of their setting they may not show actual behavior. Classification on the Basis of Mode of Administration – This includes: monitors and records the behavior as it occurs. The recording is done on an observation schedule. The personal observation not only records what, has been specified but also identifies and records unexpected behaviors that defy pre-established response categories. Mechanical Observation – Mechanical devices, instead of human”s are to record the behavior. The devices record the behavior as it occurs and data is sorted and analyzed later on. Apart from cameras, other devices are galvanometer which measures the emotional arousal induced by an exposure to a specific stimuli, audiometer and people meter that record which channel on TV is being viewed with the latter also recording who is viewing the channel, coulometer records the eye movement etc. Audit – It is the process of obtaining information by physical examination of data. The audit, which is a count of physical objects, is generally done by the researcher himself. An audit can be a store audit or a pantry audit. The store audits are performed by the distributors or manufacturers in order to ana1yse the market share, purchase pattern etc. e.g. the researcher may check the store records or do an analysis of inventory on hand to record the data. The pantry audit involves the researcher developing an inventory of brands quantities and package sizes of products in a consumer”s home, generally in the course of a personal interview. Such an audit is used to supplement or test the truthfulness of information provided in the direct questionnaire. Content

Statistics – Geometric Probability Distribution ”; Previous Next The geometric distribution is a special case of the negative binomial distribution. It deals with the number of trials required for a single success. Thus, the geometric distribution is a negative binomial distribution where the number of successes (r) is equal to 1. Formula ${P(X=x) = p times q^{x-1} }$ Where − ${p}$ = probability of success for single trial. ${q}$ = probability of failure for a single trial (1-p) ${x}$ = the number of failures before a success. ${P(X-x)}$ = Probability of x successes in n trials. Example Problem Statement: In an amusement fair, a competitor is entitled for a prize if he throws a ring on a peg from a certain distance. It is observed that only 30% of the competitors are able to do this. If someone is given 5 chances, what is the probability of his winning the prize when he has already missed 4 chances? Solution: If someone has already missed four chances and has to win in the fifth chance, then it is a probability experiment of getting the first success in 5 trials. The problem statement also suggests the probability distribution to be geometric. The probability of success is given by the geometric distribution formula: ${P(X=x) = p times q^{x-1} }$ Where − ${p = 30 % = 0.3 }$ ${x = 5}$ = the number of failures before a success. Therefore, the required probability: $ {P(X=5) = 0.3 times (1-0.3)^{5-1} , \[7pt] , = 0.3 times (0.7)^4, \[7pt] , approx 0.072 \[7pt] , approx 7.2 % }$ Print Page Previous Next Advertisements ”;

Statistics – Factorial ”; Previous Next Factorial is a function applied to natural numbers greater than zero. The symbol for the factorial function is an exclamation mark after a number, like this: 2! Formula ${n! = 1 times 2 times 3 … times n}$ Where − ${n!}$ = represents factorial ${n}$ = Number of sets Example Problem Statement: Calculate the factorial of 5 i.e. 5!. Solution: Multiply all the whole numbers up to the number considered. ${5! = 5 times 4 times 3 times 2 times 1 , \[7pt] , = 120}$ Print Page Previous Next Advertisements ”;

Statistics – Notations ”; Previous Next Following table shows the usage of various symbols used in Statistics Capitalization Generally lower case letters represent the sample attributes and capital case letters are used to represent population attributes. $ P $ – population proportion. $ p $ – sample proportion. $ X $ – set of population elements. $ x $ – set of sample elements. $ N $ – set of population size. $ N $ – set of sample size. Greek Vs Roman letters Roman letters represent the sample attributs and greek letters are used to represent Population attributes. $ mu $ – population mean. $ bar x $ – sample mean. $ delta $ – standard deviation of a population. $ s $ – standard deviation of a sample. Population specific Parameters Following symbols represent population specific attributes. $ mu $ – population mean. $ delta $ – standard deviation of a population. $ {mu}^2 $ – variance of a population. $ P $ – proportion of population elements having a particular attribute. $ Q $ – proportion of population elements having no particular attribute. $ rho $ – population correlation coefficient based on all of the elements from a population. $ N $ – number of elements in a population. Sample specific Parameters Following symbols represent population specific attributes. $ bar x $ – sample mean. $ s $ – standard deviation of a sample. $ {s}^2 $ – variance of a sample. $ p $ – proportion of sample elements having a particular attribute. $ q $ – proportion of sample elements having no particular attribute. $ r $ – population correlation coefficient based on all of the elements from a sample. $ n $ – number of elements in a sample. Linear Regression $ B_0 $ – intercept constant in a population regression line. $ B_1 $ – regression coefficient in a population regression line. $ {R}^2 $ – coefficient of determination. $ b_0 $ – intercept constant in a sample regression line. $ b_1 $ – regression coefficient in a sample regression line. $ ^{s}b_1 $ – standard error of the slope of a regression line. Probability $ P(A) $ – probability that event A will occur. $ P(A|B) $ – conditional probability that event A occurs, given that event B has occurred. $ P(A”) $ – probability of the complement of event A. $ P(A cap B) $ – probability of the intersection of events A and B. $ P(A cup B) $ – probability of the union of events A and B. $ E(X) $ – expected value of random variable X. $ b(x; n, P) $ – binomial probability. $ b*(x; n, P) $ – negative binomial probability. $ g(x; P) $ – geometric probability. $ h(x; N, n, k) $ – hypergeometric probability. Permutation/Combination $ n! $ – factorial value of n. $ ^{n}P_r $ – number of permutations of n things taken r at a time. $ ^{n}C_r $ – number of combinations of n things taken r at a time. Set $ A Cap B $ – intersection of set A and B. $ A Cup B $ – union of set A and B. $ { A, B, C } $ – set of elements consisting of A, B, and C. $ emptyset $ – null or empty set. Hypothesis Testing $ H_0 $ – null hypothesis. $ H_1 $ – alternative hypothesis. $ alpha $ – significance level. $ beta $ – probability of committing a Type II error. Random Variables $ Z $ or $ z $ – standardized score, also known as a z score. $ z_{alpha} $ – standardized score that has a cumulative probability equal to $ 1 – alpha $. $ t_{alpha} $ – t statistic that has a cumulative probability equal to $ 1 – alpha $. $ f_{alpha} $ – f statistic that has a cumulative probability equal to $ 1 – alpha $. $ f_{alpha}(v_1, v_2) $ – f statistic that has a cumulative probability equal to $ 1 – alpha $ and $ v_1 $ and $ v_2 $ degrees of freedom. $ X^2 $ – chi-square statistic. Summation Symbols $ sum $ – summation symbol, used to compute sums over a range of values. $ sum x $ or $ sum x_i $ – sum of a set of n observations. Thus, $ sum x = x_1 + x_2 + … + x_n $. Print Page Previous Next Advertisements ”;