Stats for Data Science Flashcards
Descriptive Analytics
Leveraging historical data to determine “What” happened.
Predictive Analytics
Leveraging historical data to determine “What will” happen.
Prescriptive Analytics
Based on information gained from predictive analytics, the information is used to determine “What will we do”.
Probability
The measure of the likelihood that an event will occur based on a random experiment.
Complement
P(A) + P(A’) = 1
Intersection
P(A∩B)=P(A)P(B) Set off all elements that are members of both A and B.
Union
P(A∪B)=P(A)+P(B)−P(A∩B) Set of all elements in the collection.
Conditional Probability
P(A|B) is a measure of the probability of one event occurring with some relationship to one or more other events.
Independent Events
Two events are independent if the occurrence of one does not affect the probability of occurrence of the other.
Mutually Exclusive Events
Two events are mutually exclusive if they cannot both occur at the same time.
Bates’ Theorem
Bayes’ Theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event.
Mean
The average of the dataset.
Median
The middle value of an ordered dataset.
Mode
The most frequent value in the dataset.
Skewness
A measure of symmetry.
Kurtosis
A measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution
Range
The difference between the highest and lowest value in the dataset.
Interquartile Range
IQR = Q3−Q1
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.
Standard Error
An estimate of the standard deviation of the sampling distribution.
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 Mass Function
A function that gives the probability that a discrete random variable is exactly equal to some value.
Probability Density Function
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
A function that gives the probability that a random variable is less than or equal to a certain value.
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 bell-shaped 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.
Central Limit Theorem
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.
Chi-Squared Distribution
The distribution of the sum of squared standard normal deviates.
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 (1-p).
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 (1-p).
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.
Null Hypothesis
A general statement that there is no relationship between two measured phenomena or no association among groups.
Alternative Hypothesis
Contrary to the null hypothesis.
Type 1 Error
rejection of a true null hypothesis.
Type 2 Error
the non-rejection of a false null hypothesis.
P-Value
When p-value > α, we fail to reject the null hypothesis, while p-value ≤ α, we reject the null hypothesis and we can conclude that we have the 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.
Significance Level & Rejection Region
The rejection region is actually depended on the significance level. The significance level is denoted by α and is the probability of rejecting the null hypothesis if it is true.
Z-Score
finds the distance from the sample’s mean to an individual data point expressed in units of standard deviation. (Large sample size)
T - Score
A T-test 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.
1 -Way ANOVA
compare two means from tow independent group using only one independent variable.
2 -Way ANOVA
is the extension of one-way ANOVA using two independent variables to calculate main effect and interaction effect.
Chi -Square Goodness of Fit Test
determine if a sample matches the population fit one categorical variable to a distribution.
Chi -Square Test for Independence
compare two sets of data to see if there is a relationship.
Linear Regression
is a linear approach to modeling the relationship between a dependent variable and one independent variable.
Independent Variable
is the variable that is controlled in a scientific experiment to test the effects on the dependent variable.
Dependent Variable
is the variable being measured in a scientific experiment.
Multiple Linear Regression
is a linear approach to modeling the relationship between a dependent variable and two or more independent variables.
Linear Regression: Step#1
Understand the model description, causality and directionality
Linear Regression: Step#2
Check the data, categorical data, missing data and outliers
Linear Regression: Step#3
Simple Analysis — Check the effect comparing between dependent variable to independent variable and independent variable to independent variable
Linear Regression: Step#4
Multiple Linear Regression — Check the model and the correct variables
Linear Regression: Step#5
Residual Analysis: Check normal distribution and normality for the residuals.
Linear Regression: Step#5
Interpretation of Regression Output: R-Squared is a statistical measure of fit that indicates how much variation of a dependent variable is explained by the independent variables. Higher R-Squared value represents smaller differences between the observed data and fitted values.
- P - Value
- Regression Equation
