Primer on Statistics -I

Pervasive phobia of numbers is complicated by the pedagogical approaches bordering on the abstract towards mathematics, statistics and related subjects. Yet, many concepts or the principles underlying the concepts can be understood without resorting to numbers. There are two dimensions in understanding statistics. The first is conceptual understanding or the significance of the test, or and statistical principle. Secondly, it is the operational element- the use of the same in practice. The latter is emphasized through the pedagogy and obviously needs mastery of numeric. Yet, without the former, very little progress can happen in the latter. The conceptual understanding is possible without resorting to any sort of numerical gymnastics by taking refuge in principles navigated consciously or sub consciously in day to day life.

It makes sense to construct a tabular model to understand the conceptual applications of various statistical tools.

Statistical tool/ test/ measure	Applications or when should it be used
Variance	Using metro for conveyance would basically ensure timings are certain and unlikely to change every day. Yet commuting by buses would result in different timing every day. It is because of road traffic, signals, condition of road etc. how does one determine the route time of the bus? How much time be allocated to each trip. Here not just the average but the variance might be of help. Does all trips correspond closely to average or deviate sharply from the average. Higher deviations necessitates higher slack. Similarly for producing goods that volatile demand. At times high and at other times low. Variance helps in demand forecasting and thus production planning
Standard deviation	Similar to variation. Example could be planning the financial portfolio. How the returns correspond to the market return. What is the deviation from the mean? Significant deviation implies greater uncertainty.
Chi-square	When or does observed reality differs from what is expected   Differences in voting behaviour between men and women; Are women better salespersons that men; Do women perform better in academics; Swiggy prices better than Zomato or vice versa; Uber drivers better than Ola or vice versa
t-test	We are adding some qualification to chi-square test. For example are women better performers in academics than men in STEM subjects- note there is addition to previous problem (comparing in field of STEM; Are Swiggy prices better than Zomato in peak hours ; Ola prices better than Uber in peak hours; line productivity better than staff productivity in IT industry
ANOVA	When performing analysis on groups which have difference within groups or across groups Does economics scores differ between Sec A, B and C? Are state populations homogenous or heterogeneous- ex; Tamil Nadu might have homogenous population yet in J&K significant differences exists between regions. To a similar extent Assam where difference across sub geographies create grounds for demand of separate state Is there significant difference among productivity of employees of Infosys between its Bangalore, Pune and Hyderabad offices Do different income groups exhibit differences in buying behaviour
Pearson Correlation	Used in trying to establish relationship between two different variables. Does one result in the similar or opposite movement of the other Which stock to purchase. There are some stocks which routinely behave the opposite of the market movement. If market is up, these go down and vice versa. To hedge, identification of these stocks is necessary. Correlation is used in such scenarios. Those demonstrating negative correlation to the market are selected Rainfall level and agricultural production Cyclone in Bay of Bengal and rainfall in South Karnataka Violation of traffic rules and accidents Sales of each team member and overall sales
Coefficient of determination	Any variable is susceptible to influences from multiple variables. Capture of all the variables cannot happen. Yet coefficient of determination can help is finding how much of influence does all dependent variables exert on the independent variable in question. The output of the firm is dependent on the individual productivity. Yet it might not be the only factor. There could be delivery of raw material by vendors on time (vendor productivity), performance of machines (might be maintenance issues etc) etc.  To enable, collective influence of all these variables, coefficient of determination comes handy Rent of a flat explained by age of building, floor in which is located, area of location, total super-built area in sq feet, number of rooms etc
Multiple regression	Sales of firm might be influenced by factors ranging from product quality, distribution network, advertising, promo campaigns, brand awareness etc. Some might have influenced, yet in some cases, it might be chance occurrence. Is the increase in sales on account of increase in advertising, promo campaigns or is it merely chance occurrence. There could be potential fallacy that increase promo campaigns might have caused increased sales. To confirm or demolish such assertions, statistics offers a tool called multiple regression wherein the dependent variable is tested against the influence of multiple independent variables Similarly, economic growth linked to income levels, inflation levels, price levels etc Also train punctuality linked to traffic density, single or double line, driving style, station capacity, operational constraints etc
Cardinal scaling	Understanding people’s preferences and the need to create uniformity across the sample necessitates scaling. Cardinal scale is about their feelings on any attribute on raw scale. On a scale of 1-10, how much would a car owner to the brand of car he/she owns. If a person is asked how do they rate their experience on scale of 1-10 in various restaurants and malls. How do they rate their consumer durable on scale of 1-10 or 1-5 etc. highest number in the scale is maximum rating, the lowest number is minimum rating.
Ordinal scaling	Used to rank importance of attributes. How does one rank all the brands of television sets or mobile handsets or even mobile service providers? How one rank different does attributes in order of their importance when purchasing a car or two wheeler or a flat?
Heat Maps	Used in identifying an intensity of phenomena. Heat maps used to used to pin point the location of epidemics by mapping the geographies from cases are reported. If there is malaria or cholera etc where are the cases coming from? Which areas are they getting reported from. Heat maps best represent the same thus good aid for redressing the epidemic. Similarly for the crime spots (where are the crimes happening and frequency of the  crime), accident spots, traffic densities, people movement in public spaces