Month: January 2021

Statistics for Beginners in Excel – Central Limit Theorem

(Basic Statistics for Citizen Data Scientist) Central Limit Theorem Theorem 1 – Central Limit Theorem: If x has a distribution with mean μ and standard deviation σ then for n sufficiently large, the variable has a distribution which is approximately the standard normal distribution. Observation: The larger the value of n the better the approximation will be. For practical purposes when n ≥ 30, then the approximation will be …

Statistics for Beginners in Excel – Confidence Intervals for Sampling Distributions

(Basic Statistics for Citizen Data Scientist) Confidence Intervals for Sampling Distributions Suppose we take a sample of size n from a normal population N(μ, σ) and ask whether the sample mean differs significantly from the overall population mean. As we have seen in Single Sample Hypothesis Testing The exact point of rejection (at the right tail), zcrit, has value And so …

Statistics for Beginners in Excel – Standardized Effect Size

(Basic Statistics for Citizen Data Scientist) Standardized Effect Size Definition 1: Cohen’s d, a statistic which is independent of the sample size and is defined as where m1 and m2 represent two means and σpooled is some combined value for the standard deviation. The effect size given by d is conventionally viewed as small, medium or large as follows:  d = 0.20 – small effect  d = …

Statistics for Beginners in Excel – Single Sample Hypothesis Testing

(Basic Statistics for Citizen Data Scientist) Single Sample Hypothesis Testing Suppose we take a sample of size n from a normal population N(μ, σ) and ask whether the sample mean differs significantly from the overall population mean. This is equivalent to testing the following null hypothesis H0: We use a two-tailed hypothesis, although sometimes a one-tailed hypothesis is preferred …

Statistics for Beginners in Excel – Sampling Distributions

(Basic Statistics for Citizen Data Scientist) Basic Concepts of Sampling Distributions Definition 1: Let x be a random variable with normal distribution N(μ, σ). Now consider a random sample {x1, x2,…, xn} from this population. The mean of the sample (called the sample mean) is x̄ can be considered to be a number representing the mean of the actual sample taken, …

Statistics for Beginners in Excel – Truncated Normal Distribution

(Basic Statistics for Citizen Data Scientist) Truncated Normal Distribution Definition 1: Let -∞ ≤ a < b ≤ ∞. Then the pdf of the truncated normal distribution with mean μ and variance σ2 constrained by  is where φ is the pdf of the normal distribution and Φ is the cdf of the normal distribution. We assume that if x < a or x = -∞ then φ(x, µ, σ) = 0 and …

Statistics for Beginners in Excel – Log-normal Distribution

(Basic Statistics for Citizen Data Scientist) Log-normal Distribution Definition 1: A random variable x is log-normally distributed provided the natural log of x, ln x, is normally distributed. The probability density function (pdf) of the log-normal distribution is Observation: Some key statistical properties are:   Observation: Sometimes it is useful to use a transformation of the population being studied. In particular, …

Statistics for Beginners in Excel – Standard Normal Distribution

(Basic Statistics for Citizen Data Scientist) Standard Normal Distribution Definition 1: The standard normal distribution is N(0, 1). To convert a random variable x with normal distribution N(μ, σ) to standard normal form you use the following linear transformation: The resulting random variable is called a z-score. Thus z = STANDARDIZE(x, μ, σ), as described in Definition 3 and Excel Functions in Expectation. Figure …