The 8 Basic Statistics Concepts for Data Science
Understanding the fundamentals of statistics is a core capability for becoming a Data Scientist. Review these essential ideas that will be pervasive in your work and raise your expertise in the field.
By Shirley Chen, MSBA in ASU  Data Analyst.
Statistics is a form of mathematical analysis that uses quantified models and representations for a given set of experimental data or reallife studies. The main advantage of statistics is that information is presented in an easy way. Recently, I reviewed all the statistics materials and organized the 8 basic statistics concepts for becoming a data scientist!
 Understand the Type of Analytics
 Probability
 Central Tendency
 Variability
 Relationship Between Variables
 Probability Distribution
 Hypothesis Testing and Statistical Significance
 Regression
Understand the Type of Analytics
Descriptive Analytics tells us what happened in the past and helps a business understand how it is performing by providing context to help stakeholders interpret information.
Diagnostic Analytics takes descriptive data a step further and helps you understand why something happened in the past.
Predictive Analytics predicts what is most likely to happen in the future and provides companies with actionable insights based on the information.
Prescriptive Analytics provides recommendations regarding actions that will take advantage of the predictions and guide the possible actions toward a solution.
Probability
Probability is the measure of the likelihood that an event will occur in a Random Experiment.
Complement: P(A) + P(A’) = 1
Intersection: P(A∩B) = P(A)P(B)
Union: P(A∪B) = P(A) + P(B) − P(A∩B)
Intersection and Union.
Conditional Probability: P(AB) is a measure of the probability of one event occurring with some relationship to one or more other events. P(AB)=P(A∩B)/P(B), when P(B)>0.
Independent Events: Two events are independent if the occurrence of one does not affect the probability of occurrence of the other. P(A∩B)=P(A)P(B) where P(A) != 0 and P(B) != 0 , P(AB)=P(A), P(BA)=P(B)
Mutually Exclusive Events: Two events are mutually exclusive if they cannot both occur at the same time. P(A∩B)=0 and P(A∪B)=P(A)+P(B).
Bayes’ Theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event.
Bayes’ Theorem.
Central Tendency
Mean: The average of the dataset.
Median: The middle value of an ordered dataset.
Mode: The most frequent value in the dataset. If the data have multiple values that occurred the most frequently, we have a multimodal distribution.
Skewness: A measure of symmetry.
Kurtosis: A measure of whether the data are heavytailed or lighttailed relative to a normal distribution
Variability
Range: The difference between the highest and lowest value in the dataset.
Percentiles, Quartiles and Interquartile Range (IQR)
 Percentiles — A measure that indicates the value below which a given percentage of observations in a group of observations falls.
 Quantiles— Values that divide the number of data points into four more or less equal parts, or quarters.
 Interquartile Range (IQR)— A measure of statistical dispersion and variability based on dividing a data set into quartiles. IQR = Q3 − Q1
Percentiles, Quartiles and Interquartile Range (IQR).
Variance: The average squared difference of the values from the mean to measure how spread out a set of data is relative to mean.
Standard Deviation: The standard difference between each data point and the mean and the square root of variance.
Population and Sample Variance and Standard Deviation.
Standard Error (SE): An estimate of the standard deviation of the sampling distribution.
Population and Sample Standard Error.
Relationship Between Variables
Causality: Relationship between two events where one event is affected by the other.
Covariance: A quantitative measure of the joint variability between two or more variables.
Correlation: Measure the relationship between two variables and ranges from 1 to 1, the normalized version of covariance.
Probability Distributions
Probability Distribution Functions
Probability Mass Function (PMF): A function that gives the probability that a discrete random variable is exactly equal to some value.
Probability Density Function (PDF): A function for continuous data where the value at any given sample can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
Cumulative Density Function (CDF): A function that gives the probability that a random variable is less than or equal to a certain value.
Comparison between PMF, PDF, and CDF.
Continuous Probability Distribution
Uniform Distribution: Also called a rectangular distribution, is a probability distribution where all outcomes are equally likely.
Normal/Gaussian Distribution: The curve of the distribution is bellshaped and symmetrical and is related to the Central Limit Theorem that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger.
Exponential Distribution: A probability distribution of the time between the events in a Poisson point process.
ChiSquare Distribution: The distribution of the sum of squared standard normal deviates.
Discrete Probability Distribution
Bernoulli Distribution: The distribution of a random variable which takes a single trial and only 2 possible outcomes, namely 1(success) with probability p, and 0(failure) with probability (1p).
Binomial Distribution: The distribution of the number of successes in a sequence of n independent experiments, and each with only 2 possible outcomes, namely 1(success) with probability p, and 0(failure) with probability (1p).
Poisson Distribution: The distribution that expresses the probability of a given number of events k occurring in a fixed interval of time if these events occur with a known constant average rate λ and independently of the time.
Hypothesis Testing and Statistical Significance
Null and Alternative Hypothesis
Null Hypothesis: A general statement that there is no relationship between two measured phenomena or no association among groups. Alternative Hypothesis: Be contrary to the null hypothesis.
In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis, while a type II error is the nonrejection of a false null hypothesis.
Interpretation
Pvalue: The probability of the test statistic being at least as extreme as the one observed given that the null hypothesis is true. When pvalue > α, we fail to reject the null hypothesis, while pvalue ≤ α, we reject the null hypothesis, and we can conclude that we have a significant result.
Critical Value: A point on the scale of the test statistic beyond which we reject the null hypothesis and is derived from the level of significance α of the test. It depends upon a test statistic, which is specific to the type of test, and the significance level, α, which defines the sensitivity of the test.
Significance Level and Rejection Region: The rejection region is actually dependent on the significance level. The significance level is denoted by α and is the probability of rejecting the null hypothesis if it is true.
ZTest
A Ztest is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution and tests the mean of a distribution in which we already know the population variance. Therefore, many statistical tests can be conveniently performed as approximate Ztests if the sample size is large or the population variance is known.
TTest
A Ttest is the statistical test if the population variance is unknown, and the sample size is not large (n < 30).
Paired sample means that we collect data twice from the same group, person, item, or thing. Independent sample implies that the two samples must have come from two completely different populations.
ANOVA (Analysis of Variance)
ANOVA is the way to find out if experimental results are significant. Oneway ANOVA compares two means from two independent groups using only one independent variable. Twoway ANOVA is the extension of oneway ANOVA using two independent variables to calculate the main effect and interaction effect.
ANOVA Table.
ChiSquare Test
ChiSquare Test Formula.
ChiSquare Test checks whether or not a model follows approximately normality when we have s discrete set of data points. Goodness of Fit Test determines if a sample matches the population fit one categorical variable to a distribution. ChiSquare Test for Independence compares two sets of data to see if there is a relationship.
Regression
Linear Regression
Assumptions of Linear Regression
 Linear Relationship
 Multivariate Normality
 No or Little Multicollinearity
 No or Little Autocorrelation
 Homoscedasticity
Linear Regression is a linear approach to modeling the relationship between a dependent variable and one independent variable. An independent variable is a variable that is controlled in a scientific experiment to test the effects on the dependent variable. A dependent variable is a variable being measured in a scientific experiment.
Linear Regression Formula.
Multiple Linear Regression is a linear approach to modeling the relationship between a dependent variable and two or more independent variables.
Multiple Linear Regression Formula.
Steps for Running the Linear Regression
Step 1: Understand the model description, causality, and directionality
Step 2: Check the data, categorical data, missing data, and outliers
 Outlier is a data point that differs significantly from other observations. We can use the standard deviation method and interquartile range (IQR) method.
 Dummy variable takes only the value 0 or 1 to indicate the effect for categorical variables.
Step 3: Simple Analysis — Check the effect comparing between dependent variable to independent variable and independent variable to independent variable
 Use scatter plots to check the correlation
 Multicollinearity occurs when more than two independent variables are highly correlated. We can use Variance Inflation Factor (VIF) to measure if VIF > 5 there is highly correlated and if VIF > 10, then there is certainly multicollinearity among the variables.
 Interaction Term implies a change in the slope from one value to another value.
Step 4: Multiple Linear Regression — Check the model and the correct variables
Step 5: Residual Analysis
 Check normal distribution and normality for the residuals.
 Homoscedasticity describes a situation in which the error term is the same across all values of the independent variables and means that the residuals are equal across the regression line.
Step 6: Interpretation of Regression Output
 RSquared is a statistical measure of fit that indicates how much variation of a dependent variable is explained by the independent variables. Higher RSquared value represents smaller differences between the observed data and fitted values.
 Pvalue
 Regression Equation
Original. Reposted with permission.
Bio: Shirley Chen is a Business Intelligence Analyst at UHaul and recent graduate with a Master's Degree in MSBusiness Analytics from ASU.
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