Hits: 5 (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 …

# Month: January 2021

Hits: 2 (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 …

Hits: 4 (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 …

Hits: 5 (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 …

Hits: 2 (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 …

Hits: 1 (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) …

Hits: 2 (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. …

Hits: 6 (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 …

Hits: 8 Year 1 – Math Worksheet 004 – Counting Numbers 1-100 (by ones) Year 1 – Math Worksheet 001 – Decomposition of Numbers within 10 Free Machine Learning & Data Science Coding Tutorials in Python & R for Beginners. Subscribe @ Western Australian Center for Applied Machine Learning & Data Science. Western …

Hits: 5 Year 1 – Math Worksheet 003 – Understanding Measurements Length and Width of an Object Year 1 – Math Worksheet 002 – Properties of Shapes Free Machine Learning & Data Science Coding Tutorials in Python & R for Beginners. Subscribe @ Western Australian Center for Applied Machine Learning & Data Science. …

Hits: 6 (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 …

Hits: 8 (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 …

Hits: 3 (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 …

Hits: 8 (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 …

Hits: 6 (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 …

Hits: 7 (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 …