Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of data
Vector Space Let \(V\) be a set with cardinality at least 2 and let \((V,+)\) be an Abelian group with respect to the operation \(+\). Let \(\mathbb{R}\) be the field of real numbers. For any \(c\in\mathbb{R}\) and \(v\in V\), define \(c\cdot v = 0\), where \(0\) is the identity element in the Abelian group \((V,+)\). […]
ADAS – Advanced Driver Assistance Systems are electronic systems designed to enhance vehicle safety and driving comfort by assisting drivers with various tasks. These systems use sensors, cameras, and other technologies to monitor the vehicle’s surroundings and provide warnings or automated actions to prevent accidents In the rapidly evolving world of autonomous and semi-autonomous driving, ADAS play
Digital transformation is about survival. Companies that upskill strategically, start small but think big, and measure everything will dominate the next decade. In India, combining Jugaad innovation with AI precision positions enterprises to leapfrog legacy systems. With global automakers sourcing 34% more AI solutions from India, the window is open. Will you lead or follow?
A binomial test uses sample data to evaluate Hypothesis about the values of p and q for a population consisting of binomial data.
The measurement scale consists of exactly two categories
Each individual observation in a sample is classified in only one of the two categories
Sample data consist of the frequency or number of individuals in each category
The chi-square test for goodness of fit uses sample data to test hypotheses about the shape or proportions of a population distribution. The test determines how well the obtained sample proportions fit the population proportions specified by the null hypothesis.
The observed frequency is the number of individuals from the sample who are classified in a particular category. Each individual is counted in one and only one category.
The statistical technique for finding the best-fitting straight line for a set of data is called regression, and the resulting straight line is called the regression line.
The goal for regression is to find the best-fitting straight line for a set of data.
Y = bX + a, best fit is define precisely to achieve the above goal. b and a are constants that determine the slope and Y-intercept of the line
The Pearson correlation measures the degree and the direction of the linear relationship between two variables.
The Pearson correlation for a sample is identified by the letter r. The corresponding correlation for the entire population is identified by the Greek letter rho (ρ), which is the Greek equivalent of the letter r
More than one factor analysis is called a factorial design
ANOVA with two independent variables is called a two-factor design.
Such a design can be presented in a table with the levels of one factor defining the rows and the levels of the other factor defining the columns.
Each cell in the matrix corresponds to a specific combination of the two factors.
An independent variable is manipulated to create two or more treatment conditions, with the same group of participants compared in all of the experiments.
Study with same group of individuals by observing at two or more different times.
It is is a hypothesis-testing procedure that is used to evaluate mean differences between two or more treatments (or populations).
ANOVA uses sample data as the basis for drawing general conclusions about populations.
t tests are limited to situations in which there are only two treatments to compare.
ANOVA can be used to compare two or more treatments.
A design that uses two sets of data that are obtained from the same group of participants, is called a repeated-measures research design or a within-subjects design.
In a related-samples research study, the individuals in one treatment condition are directly related, one-to-one, with the individuals in the other treatment condition(s).
The Independent Samples t test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different
A hypothesis test determines whether the treatment effect is greater than chance, where “chance” is measured by the standard error.
H0 the null hypothesis states that the treatment has no effect.
The t statistic is used to test hypotheses about an unknown population mean, μ, when the value of σ is unknown.
The formula for the t statistic has the same structure as the z-score formula, except that the t statistic uses the estimated standard error in the denominator
The power of a statistical test is the probability that the test will correctly reject a false null hypothesis.
The power is defined as the probability that the test will reject the null hypothesis if the treatment really has an effect
In a directional hypothesis test, or a one-tailed test, the statistical hypotheses (H0 and H1) specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.
In a hypothesis test, there are two different kinds of errors that can be made.
A Type I error occurs when Null hypothesis is rejected when it was actually true. In this error analysis concludes that a treatment does have an effect when in fact it has no effect.
Hypothesis testing is a statistical procedure that helps us to draw inferences about the population by using sample data.
Hypothesis test is a method of making decisions or inferences from sample data (evidence)
Bernoulli Distribution
Uniform Distribution
Binomial Distribution
Normal Distribution
Poisson Distribution
Exponential Distribution
Descriptive statistics summarize and organize characteristics of a data set/entire population.
The point-biserial correlation is a special case of correlation in which one variable is continuous and the other variable is binary (dichotomous).
Population is the set of all individuals of interest in a particular study.
A sample is a subgroup of the population.
Measurement is a process of assigning numbers/values to a physical condition, phenomena or status. There are four different scales of measurement. The data can be defined as being one of the four scales.
Statistics may be called the science of counting , Data are individual pieces of factual information collected for the purpose of analysis, In statistical research, a variable is defined as an attribute of an object of study
