Research Statistics: Scratch to Master

Explore data visualization basics using line charts to compare laptop and tablet sales from January to June, and understand simple versus multiple line charts for presenting insights to management.

Explore the main bar diagram types—simple and multiple bars, stacked bars, and horizontal bars—emphasizing their uses in manpower planning and cross-country comparisons, such as beer consumption.

Watch a video explanation of the application of bar charts in research statistics, guiding learners from scratch to mastery.

Learn to represent monthly expenses with a pie chart using angle and percentage methods, detailing groceries, transport, electricity, school fees, and savings from a 15,000 rupee budget.

Master tabulation by understanding table types, captions, dates, headings, units, footnotes, and sources, and prepare data for analysis using tools like SPSS.

Learn how to construct a frequency distribution by dividing data into class intervals, determine range, set class boundaries, and tally frequencies to build a clear distribution table.

Explore visualizing a frequency distribution with histogram, frequency polygon, and cumulative frequency, including converting discrete data to continuous class intervals, computing midpoints, and identifying the mode from the graph.

Learn how to calculate the mode from a histogram with continuous class intervals by identifying the highest frequency bar and estimating the mode within 43.5 to 55.5, about 49.2.

Learn how to construct a frequency polygon by plotting the midpoints of class intervals, then connecting histogram midpoints to form a continuous, complete polygon.

Explore how ogives are used to calculate the median from a frequency distribution, using less-than and greater-than cumulative frequencies and class boundaries to locate the median.

Explore ogives (continued) and reading class boundaries within class intervals, plot cumulative frequencies on graph paper, and determine the median from the graphical limit.

Explore types of frequency curves, including histograms and frequency polygons, with smooth and parabola-like shapes, and applications to product lifecycles and population growth.

Explore how dispersion measures describe data spread in descriptive statistics, comparing absolute and relative approaches using range, mean deviation, standard deviation, and variance, with relative measures expressed in percentage.

Compute the data range by subtracting the minimum from the maximum, 22 minus 3, yielding 19, and express the coefficient of range as (max−min)/(max+min)×100%, yielding 76%.

Explore quartile deviation for grouped data with continuous class intervals using Q1, Q3, and cumulative frequency. Compute the coefficient of quartile deviation from Q1 and Q3 using the formulas.

Learn to calculate quartile values from open-ended class intervals using cumulative frequencies, converting to frequencies, and identify Q1 and Q3 for data analysis.

Explain mean deviation from the center with deviations from mean, median, or mode. State the coefficient of mean deviation as deviation about M divided by M, in percent.

Learn to compute the median from grouped data using cumulative frequencies and class intervals, identify the median class, and then determine the mean deviation about the median and its coefficient.

Explore the standard deviation, a core concept in descriptive statistics, why we square deviations from the mean, and formulas for raw data and frequency distributions.

Learn to compute the composite standard deviation for two groups by using group means and standard deviations, and apply the combined mean formula, as shown in the example.

Explore how to compute the coefficient of variation by dividing standard deviation by the mean and multiplying by 100 to express it as a percentage, assessing data consistency.

Compare two batsmen using the coefficient of variance to assess consistency and guide national team selection for the upcoming tournament.

Learn to compute the coefficient of variance from a missing frequency in a grouped distribution. Use mean 16.4 and total 72 to determine the missing frequency and the CV.

Learn to correct the mean and standard deviation when a data entry is wrong, using a 100-observation example to obtain a corrected mean of 39.70 and standard deviation of 10.62.

Discover the expected value of a random variable, the population mean μ, and how to compute variance and standard deviation, with linear transformations like y = a + b x.

Compute the expected value of a random variable by modeling a coin tossed three times, deriving population mean, variance, and standard deviation from head-count probabilities.

Explore correlation analysis between two variables, identifying independent and dependent variables, and using Pearson and Spearman methods to gauge direction and strength, with regression addressing causality.

Explore scatter diagrams to analyze correlation between variables, identify dependent and independent roles, and interpret positive, negative, or no correlation with a best fit line.

Explore Karl Pearson's correlation coefficient using Culberson's product moment, through two formulas that connect X and Y via deviations from their means and their product.

Compute Karl Pearson's correlation coefficient r for economics (X) and accountancy (Y), interpret a near 0.88 positive relationship, and conclude that proficiency in one subject relates to the other.

Compute the correlation coefficient for X and Y using the given data and the standard formula, and explore covariance to interpret a very high positive relationship.

Learn how covariance measures the association between two variables and how the correlation coefficient standardizes it, indicating a strong positive relationship (about 0.91) with a practical example.

Learn how to use Spearman's rank correlation coefficient to measure association in nonparametric data, ranking observations, computing d differences, and applying the corrected formula for ties.

Spearman's rank correlation is demonstrated by ranking two subjects, computing D^2, applying rho = 1 - 6 sum D^2 /(n(n^2-1)), and obtaining about 0.7515 with a positive, imperfect correlation.

Learn the coefficient of concurrent deviation, a quick sign-based method to assess directional correlation without magnitude. Use paired data and sign products, illustrated with price and demand.

Explore regression analysis, including simple, multiple, and ordinal regression, to predict outcomes and model relationships between a dependent variable and multiple independent variables.

Learn to fit a linear regression model by estimating regression line y = a + b x, with intercept, slope, and dependent and independent variables. Check correlation and assumptions.

This lecture introduces the minimum least squares method for fitting a line by minimizing the sum of squared errors, illustrated with data points and y = a + b x.

Identify regression coefficients, especially B1 and B0, using X and Y with means and standard deviations, and apply formula for predicting Y from X, aided by SPSS, Excel, or SAS.

Explore the limitations of linear regression through Ascombe's quartet, showing how outliers and data visualization affect the regression line, and how residuals and normal distribution tests reveal model validity.

Learn to estimate regression equations for x on y and y on x using the correlation coefficient and standard deviations, deriving the regression coefficients b_xy and b_yx.

Compute the correlation coefficient and regression estimates from given X or Y using means and standard deviations; predict Y from X and X from Y, with r about 0.82.

Learn how regression predicts a mother's height from her daughter's height, compute regression coefficients from centimeter-height data, and apply X and Y regression equations to estimate either height.

Determine X̄ and Ȳ from the regression equations using cross-multiplication, compute Bx and By, and state the positive correlation R around 0.6.

Compute the population correlation coefficient from the probable error formula, linking sample correlation r to population value with standard error, under random sampling and normality assumptions.

Apply the probable error formula to a correlation problem, compute the probable error for the correlation coefficient r, and determine the limits of the population correlation.

Explore the coefficient of determination (r-squared) and coefficient of non determination in regression, showing how variation in one variable is explained and how remaining variation arises from other factors.

Explore the concept of data distribution, distinguishing discrete and continuous distributions, their mass and density functions, central tendency, and common types like uniform, binomial, Poisson, normal, exponential, and beta.

Explore the uniform distribution as a discrete random variable, where each dice outcome from one to six has an equal probability of one-sixth. Next, examine the binomial distribution.

Explore the binomial distribution for two mutually exclusive outcomes in independent trials, using P(X=x)=C(n,x)p^x(1-p)^{n-x}; compute mean np and standard deviation sqrt(npq) with examples like sixteen dice rolls.

Apply the binomial distribution to problems like counting Sundays in 15 random dates, with X as Sundays, p = 1/7. Explore mean, standard deviation, mode, and combining independent binomial variables.

Explore the Poisson distribution, a discrete model for counts with average lambda, using p(x=k)=e^{-lambda} lambda^k / k!, and apply it to deliveries in a 4–5 pm interval.

Explore the Poisson distribution's application to rare events, derive lambda from conditions, and compute mean and standard deviation for Poisson random variables.

Explore the Poisson distribution with partial intervals, learning how to scale lambda for shorter time frames and calculate the probability of more than two accidents per hour.

Explore normal distribution and standard normal distribution, and learn to convert data via z-scores using mean and standard deviation. Apply percentile concepts for practical analysis.

Identify the normal distribution as a symmetric, continuous curve. Standardize it to the standard normal distribution with mean zero and unit standard deviation.

Learn how to compute a Z-score from X minus μ over σ, convert to the standard normal, and interpret the percentile using an Infosys test example.

Explore the concept of hypothesis testing, distinguishing null and alternative hypotheses, defining rejection regions and significance level, and interpreting sample statistics like x-bar to accept or reject claims.

Explore the burden of proof in hypothesis testing by contrasting population mean with the sample mean (x-bar) and noting that the null hypothesis is assumed true until disproved.

Understand how standard error measures the sample mean variability. Relate this variability to the data's standard deviation and show how the standard error is calculated from the sample data.

Explain how standard error guides hypothesis testing to decide whether the sample mean differs from the population mean, using critical value, p-value, and Vitek methods to accept or reject null.

Clarify the difference between standard deviation and standard error; standard deviation measures variation among individuals, while standard error measures variation of the sample mean, and discuss parametric versus nonparametric methods.

Learn about type i and type ii errors, false positives and false negatives, and how alpha, beta, and power relate to rejecting or not rejecting the null hypothesis.

Form and distinguish the null and alternative hypotheses correctly, using equality and inequality conventions, with examples to illustrate hypothesis testing steps.

Form null and alternative hypotheses from examples, such as mu equals 50000 rupees per square foot and mu not equal to 50000, illustrating how to frame claims as testable statistics.

Learn to identify null and alternative hypotheses and apply lower-tail, upper-tail, and two-tailed tests, determine rejection regions, and interpret simple examples of hypothesis testing.

Define the null and alternative hypotheses and determine the appropriate test and the prediction region cutoff to decide whether to reject the null.

Explore how hypothesis testing uses a significance level to control type I error and why zero percent error is impossible, guiding alpha choices and decisions to reject the null.

Learn the chi-squared test, a nonparametric distribution test that uses observed versus expected frequencies and degrees of freedom to assess goodness-of-fit, independence, and homogeneity.

Explore the chi-squared test for goodness of fit, comparing observed and expected frequencies in coin toss and dice examples, to determine bias, using degrees of freedom and critical values.

Explain the chi-square test for categorical data, including null and alternative hypotheses, expected values, and interpreting alpha levels, degrees of freedom, and proportions.

Compute chi-square goodness-of-fit to test Infosys old vs new policy effects in north-south-east-west regions, interpreting observed vs expected values, degrees of freedom, and critical value to reject null.

Learn to test coin bias with chi-square, using null and alternative hypotheses and critical values, and interpret a solved example where the null is not rejected.

Explore analysis of variance (ANOVA) to compare means across three or more groups, examining between-group and within-group variation, null vs. alternate hypotheses, and how confidence levels influence conclusions.

Understand the degree of freedom in ANOVA by calculating column and row freedoms, total freedom, and using the F distribution with a given alpha to compare against the critical value.

Compare the calculated value to the critical value using degree of freedom in ANOVA to decide the null hypothesis, guiding rejection or failure to reject and indicating the alternate hypothesis.

calculate between-group and within-group variance, and apply sum of squares and degrees of freedom to derive the F statistic in an ANOVA framework.

Compute the F critical value from the F distribution using the numerator and denominator degrees of freedom and the total sample size at the chosen confidence level.

Solve a problem of ANOVA to test if three teaching methodologies affect student marks, comparing between- and within-group variance and using a 95% confidence limit with the F distribution.

Explore how one-way, two-way, and n-way ANOVA compare the means of three or more groups with one or more independent variables and a dependent variable.

Learn how to formulate one-way and two-way anova hypotheses, including null, alternative, and interaction hypotheses, using a two-factor example of month and gender.

Identify differences among groups after a significant ANOVA result by performing post hoc tests to pinpoint which two or more means differ, and interpret the null hypothesis.

Master MANOVA, a multivariate analysis of variance for testing differences in means across two or more groups with multiple dependent variables; learn interpretation and why post hoc tests and statistical tools matter.