(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, …
(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 …
(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, …
(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 …
(Basic Statistics for Citizen Data Scientist) Basic Characteristics of the Normal Distribution Definition 1: The probability density function of the normal distribution is defined as: Here is the constant e = 2.7183…, and is the constant π = 3.1415… . The normal distribution is completely determined by the parameters µ and σ. It turns out that µ is the mean of the normal distribution and σ is …
(Basic Statistics for Citizen Data Scientist) Real Statistics Power Data Analysis Tool Real Statistics Data Analysis Tool: The Real Statistics Resource Pack supplies the Statistical Power and Sample Size data analysis tool to determine the power which results from a statistical test for a specified effect size, sample size and alpha, as well as the sample size …
(Basic Statistics for Citizen Data Scientist) Null and Alternative Hypothesis Generally to understand some characteristic of the general population we take a random sample and study the corresponding property of the sample. We then determine whether any conclusions we reach about the sample are representative of the population. This is done by choosing an estimator function for …
(Basic Statistics for Citizen Data Scientist) Dealing with Missing Data This tutorial is based on the Real Statistics Resource Pack. Another problem faced when collecting data is that some data may be missing. For example, in conducting a survey with ten questions, perhaps some of the people who take the survey don’t answer all ten …
(Basic Statistics for Citizen Data Scientist) Box Plots with Outliers Excel 2016 has added a Box and Whiskers chart capability. To access this capability for Example 1 of Creating Box Plots in Excel, highlight the data range A2:C11 (from Figure 1) and select Insert > Charts|Statistical > Box and Whiskers. The chart shown on the right side of Figure 1 will …
(Basic Statistics for Citizen Data Scientist) Outliers and Robustness One problem that we face in analyzing data is the presence of outliers, i.e. a data element that is much bigger or much smaller than the other data elements. For example, the mean of the sample {2, 3, 4, 5, 6} is 4, while the mean of …