Statistics

Question 1

What is the Central Limit Theorem? What is the importance of this? What are the assumptions for the CLT?

Answer 1

The sampling distribution of the mean is will approximately follow a normal distribution given:
Also:

1. Data must be sampled randomly
2. Samples should be independent of each other
3. The sample size should be sufficiently large (sample size > 30, sometimes 50 or 100)
4. Sample size should be not more than 10% of the population
   Also:
   The standard deviation of the sampling distribution of the mean is equal to the population standard deviation divided by the square root of the sample size
   Assumptions:

Question 2

What is a normal distribution? What are the properties?

Answer 2

A distribution that has three 3 main properties. These are that the mean, median, and mode equal each other. It is symmetric around the mean, and 50 percent of the values are on each side of the mean.

Question 3

What is a simple random sample? What are the advantages of a simple random sample? Disadvantages?

Answer 3

A randomly selected subset of a population where each member of the population has an exactly equal chance of being selected. An advantage is that little has to be known about the population in advance to conduct this sampling method. A disadvantage is that it requires that a complete list of every element in the population be obtained

Question 4

What is a population?

Answer 4

The entire group you want to draw conclusions about.

Question 5

What is a sample?

Answer 5

A subset of the population you will collect information from.

Question 6

What is systematic sampling? When should I use this?

Answer 6

A sampling method where every nth element is taken.
Ex. Taking every 1oth e

Question 7

What is convenience sampling?

Answer 7

A sampling method where the data first accessed is used (hence the term convenience).

Question 8

What is stratified sampling?

Answer 8

A sampling method that first divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.

Question 9

What is cluster sampling?

Answer 9

A sampling method that first divides the population into clusters. The clusters are randomly selected, and all elements in the selected clusters are used

Question 10

How can I test if my data is normally distributed?

Answer 10

1.QQ Plot ( Quantile vs Quantile Plot), which plots theoretical quantiles against the actual quantiles of our variable.
2. Hypothesis testing
a. Most powerful when testing for a normal distibution is the shapiro-wilks test.

Note:
If I was explaining to a general audience, I would show visually with histogram.

Question 11

What is power?

Answer 11

The odds of rejecting the null hypothesis given it is false. (1- beta) where beta is the probaility of Type 2 error.

Question 12

What is significance?

Question 13

What is a hypothesis test? Can you take me through each step?

Question 14

What is a confidence interval? How do i calculate?

Question 15

What is Anova?

Question 16

What is a random variable?

Answer 16

A function that maps values to each of an experiment’s outcomes

Question 17

What are some non-parametric statistical tests?

Answer 17

1. Kolmogorov Smirnov test, which computes the distances between the empirical distribution and the theoretical distribution and defines the test statistic as the supremum of the set of those distances.
2. The Anderson–Darling test is a statistical test of whether a given sample of data is drawn from a given probability distribution.

Question 18

What is a Bernoulli random variable? Binomial?

Answer 18

A Bernoulli random variable takes the value 1 with probability of p and the value 0 with probability of 1 − p. It is frequently used to represent binary experiments, such as a coin toss. A binomial random variable is the sum of n independent Bernoulli random variables with probability p.

Question 19

What is a geometric random variable?

Answer 19

A geometric random variable counts the number of trials that are required to observe a single success, where each trial is independent and has success probability p. For example, this distribution can be used to model the number of times a die must be rolled in order for a six to be observed.

Question 20

What is Poision random variable?

Answer 20

A Poisson random variable counts the number of events occurring in a fixed interval of time or space, given that these events occur with an average rate λ.

Question 21

What is a Negative Binomial random variable?

Answer 21

A negative binomial random variable counts the number of successes in a sequence of independent Bernoulli trials with parameter p before r failures occur. For example, this distribution could be used to model the number of heads that are flipped before three tails are observed in a sequence of coin tosses.

Question 22

What is a uninform distribution?

Answer 22

Uniform: The uniform distribution is a continuous distribution such that all intervals of equal length on the distribution’s support have equal probability. For example, this distribution might be used to model people’s full birth dates, where it is assumed that all times in the calendar year are equally likely.

Question 23

T?

Answer 23

Student T: Student’s t-distribution, or simply the t-distribution, arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

Question 24

Chi Squared?

Answer 24

Chi Squared: A chi-squared random variable with k degrees of freedom is the sum of k independent and identically distributed squared standard normal random variables. It is often used in hypothesis testing and in the construction of confidence intervals.

Question 25

Exponential?

Answer 25

Exponential: The exponential distribution is the continuous analogue of the geometric distribution. It is often used to model waiting times.

Question 26

F?

Answer 26

F: The F-distribution, also known as the Fisher–Snedecor distribution, arises frequently as the null distribution of a test statistic, most notably in the analysis of variance.

Question 27

Gamma?

Answer 27

Gamma: The gamma distribution is a general family of continuous probability distributions. The exponential and chi-squared distributions are special cases of the gamma distribution.

Question 28

Beta?

Answer 28

Beta: The beta distribution is a general family of continuous probability distributions bound between 0 and 1. The beta distribution is frequently used as a conjugate prior distribution in Bayesian statistics.

Question 29

What is bayes theorem?

Answer 29

Question 30

What is an ANOVA test?

Answer 30

A test that allows one to make comparisons between the means of three or more groups of data.
One-way: a statistical test that looks for differences of the mean while only considering one factor
Two-way: two factors (independent variables)
Advantages:
It allows comparisons to be made between three or more groups of data (most only allow for 2)
Assumptions:
1.Normality – that each sample is taken from a normally distributed population
2. Sample independence – that each sample has been drawn independently of the other samples
3. Variance equality – that the variance of data in the different groups should be the same
4. dependent variable is continuous
5. (for two-way): two independent variables should be in categorical, independent groups.
Purpose: A one-way ANOVA is primarily designed to enable the equality testing between three or more means. A two-way ANOVA is designed to assess the interrelationship of two independent variables on a dependent variable.