Regression

Question 1

Two Types of Hypothesis Types

Answer 1

• One sample Test
• Two sample Test

Question 2

What does a One sample Test determine?

Answer 2

A one-sample test determines whether or not a population parameter, like a mean or proportion, is equal to a specific value

Question 3

What does a Two Sample Test determine?

Answer 3

A two-sample test determines whether or not two population parameters, such as two means or two proportions, are equal to each other

Question 4

Steps for performing a hypothesis test

Answer 4

1. state the null hypothesis and the alternative hypothesis
2. choose a significance level
3. find the p-value
4. reject or fail to reject the null hypothesis.

Question 5

Null hypothesis

Answer 5

• is a statement that is assumed to be true unless there’s convincing evidence to the contrary.
• assumes that your observed data occurs by chance
• There is no effect in the population.
• Symbols: Equality =, ≤, ≥
• Phrases: no effect, no difference, no relationship, or no change

H0: μ = 300 (the mean weight of all produced granola bags is equal to 300 grams)

Question 6

Alternative hypothesis

Answer 6

is a statement that contradicts the null hypothesis, and is accepted as true only if there’s convincing evidence for it.

• There is an effect in the population.
• Symbols: ≠, <, >
• Phrases: an effect, a difference, a relationship, a change

Ha: μ ≠ 300 (the mean weight of all produced granola bags is not equal to 300 grams)

Question 7

significance level (α)

Answer 7

• significance level (α), represents the probability of making a Type I error.
• A significance level of five percent means you are willing to accept a five percent chance you are wrong when you reject the null hypothesis.
• typically use 5%

Question 8

P-value

Answer 8

• P-value refers to the probability of observing results as or more extreme than those observed when the null hypothesis is true.
• lower p-value means there is stronger evidence for the alternative hypothesis

Question 9

When to reject or fail to reject the null hypothesis?

Answer 9

• If your p-value is less than your significance level, you reject the null hypothesis.
• If your p-value is greater than your significance level, you fail to reject the null hypothesis.

Question 10

2 Types of Hypothesis Test Errors

Answer 10

• Type I error
• Type II error.
• A statistically significant result cannot prove with 100 percent certainty that our hypothesis is correct.
• Because hypothesis testing is based on probability, there’s always a chance of drawing the wrong conclusion about the null hypothesis.

Question 11

Type I error

Answer 11

• false positive
• occurs when you reject a null hypothesis that is actually true.
• In other words, you conclude that your result is statistically significant when in fact it occurred by chance.
• you incorrectly conclude that the medicine relieves cold symptoms when it’s actually ineffective.

Question 12

The probability of making a Type I error

Answer 12

’- significance level (α), represents the probability of making a Type I error.
- α = 5% means you are willing to accept a 5% chance you are wrong when you reject the null hypothesis.

Question 13

How to reduce Type 1 Error

Answer 13

A significance level of five percent means you are willing to accept a five percent chance you are wrong when you reject the null hypothesis.

To reduce your chance of making a Type I error, choose a lower significance level.
- from 5% to 1%

• reducing your risk of making a Type I error means you are more likely to make a Type II error, or false negative.

Question 14

Type II error

Answer 14

• false negative
• This occurs when you fail to reject a null hypothesis, which is actually false.
• In other words, you conclude your result occurred by chance when it’s in fact statistically significant.
• ex. you incorrectly conclude that the medicine is ineffective when it actually relieves cold symptoms.

Question 15

differences between the null hypothesis and the alternative hypothesis

Answer 15

• H0: typically assumes that there is no effect in the population, and that your observed data occurs by chance
• Ha: typically assumes that there is an effect in the population, and that your observed data does not occur by chance and is statistically significant.

Example
- H0: the program had no effect on sales revenue.
- Ha: the program** increased** sales revenue.

Question 16

The probability of making a Type II error

Answer 16

is called beta (β), and beta is related to the power of a hypothesis test (power = 1- β). Power refers to the likelihood that a test can correctly detect a real effect when there is one.

Question 17

How to reduce Type II Error

Answer 17

• by ensuring your test has enough power.
• In data work, power is usually set at 0.80 or 80%.
• The higher the statistical power, the lower the probability of making a Type II error.
• To increase power, you can** increase your sample size** or your significance level.

Question 18

4 Outcomes of rejecting or failing to reject H0

Answer 18

• Reject the H0 when it’s actually true (Type I error)
• Reject the H0 when it’s actually false (Correct)
• Fail to reject the H0 when it’s actually true (Correct)
• Fail to reject the H0 when it’s actually false (Type II error)

Question 19

Potential risks of Type I errors

Answer 19

A Type I error means rejecting a null hypothesis which is actually true. In general, making a Type I error often leads to implementing changes that are unnecessary and ineffective, and which waste valuable time and resources.

For example, if you make a Type I error in your clinical trial, the new medicine will be considered effective even though it’s actually ineffective. Based on this incorrect conclusion, an ineffective medication may be prescribed to a large number of people. Plus, other treatment options may be rejected in favor of the new medicine.

Question 20

Potential risks of Type II errors

Answer 20

A Type II error means failing to reject a null hypothesis which is actually false. In general, making a Type II error may result in missed opportunities for positive change and innovation. A lack of innovation can be costly for people and organizations.

For example, if you make a Type II error in your clinical trial, the new medicine will be considered ineffective even though it’s actually effective. This means that a useful medication may not reach a large number of people who could benefit from it.

Question 21

One-Sample Hypothesis Test Applications

Answer 21

• A data professional might conduct a one-sample hypothesis test to determine if a company’s average sales revenue is equal to a target value,
• a medical treatment’s average rate of success is equal to a set goal,
• or a stock portfolio’s average rate of return is equal to a market benchmark.

Question 22

One Sample Z-Test Assumptions

Answer 22

• the data is a random sample of a normally-distributed population,
• the population standard deviation is known.

Question 23

Test Statistics

Answer 23

The p-value is calculated from what’s called a test statistic.

In hypothesis testing, the test statistic is a value that shows how closely your observed data matches the distribution expected under the null hypothesis, so if you assume the null hypothesis is true and the mean delivery time is 40 minutes, the data for delivery times follows a normal distribution. The test statistic shows where your observed data, a sample mean delivery time of 38 minutes, will fall on that distribution.

Question 24

Z-Score (Hypothesis Test)

Answer 24

• Since you’re conducting a z-test, your test statistic is a z-score.
• Recall that a z-score is a measure of how many standard deviations below or above the population mean a data point is.
• Z-scores tell you where your values lie on a normal distribution.

Question 25

Z-Score: Left-Tailed Test

Answer 25

- For a normal distribution, the probability of getting a value less than your z-score of -2.82 is calculated by taking the area under the curve to the left of the z-score. - This is called a **left-tailed test** because your**p-value is located on the left tail** of the distribution. - The area under this part of the curve is the same as your **p-value**

Question 26

Z-Score: RIght-Tailed Test

Answer 26

- For a normal distribution, the probability of getting a value less than your z-score of 2.82 is calculated by taking the area under the curve to the left of the z-score. - This is called a **right-tailed test** because your**p-value is located on the right tail** of the distribution. - The area under this part of the curve is the same as your **p-value**

Question 27

Z-Score: P-value

Answer 27

0.0023 or 0.23 % This means there's a 0.23 percent probability that the difference in mean delivery time would be 2 minutes or greater if the null hypothesis is true. In other words, it's highly unlikely that their difference is due to chance.

Question 28

Two-sample Hypothesis T-tests: Means

Answer 28

- A two-sample test determines whether or not two means are equal to each other. - the **standard approach** for comparing two means.

Question 29

Two-sample t-test for means assumptions

Answer 29

- The two samples are **independent** of each other. - For each sample, the data is drawn randomly from a **normally distributed** population. - The population standard deviation is **unknown**.

Question 30

t-distribution

Answer 30

The graph of the t-distribution has a bell shape that is similar to the standard normal distribution, but the t-distribution has **bigger tails** than the standard normal distribution does. The bigger tails indicate the **higher frequency of outliers** that come with small dataset. As the **sample size increases**, the **t-distribution** approaches the **normal distribution.**

Question 31

Two-tailed test

Answer 31

Because you're interested in values in **both directions**, either less than or greater than your test statistic, your p-value is the probability of getting a value less than the T-score -1.2508 or greater than the T-score positive 1.2508. Your **p-value** corresponds to the area under the curve on both the left tail and the right tail of the distribution.

Question 32

Left vs Right vs Two Tailed Test and Alt. Hypothesis

Answer 32

- In a **left-tailed** test, Ha < 30 (mean weight of the penguin population is less than 30 lbs. - In a **right-tailed test**, Ha < 30 (mean weight of the penguin population is greater than 30 lbs.) - In a **two-tailed test**, Ha ≠ 30 (mean weight of the penguin population is not equal to 30 lbs.

Question 33

A/B testing

Answer 33

compare two versions of something to find out which version performs better.

Question 34

A/B Testing Application

Answer 34

Data professionals use A/B testing to help business leaders - optimize product performance, - improve customer experience, and - grow their online business.

Question 35

A/B test: 3 main features

Answer 35

1. Test design 2. Sampling 3. Hypothesis testing

Question 36

A/B test: Test design

Answer 36

In a **randomized controlled experiment**, test subjects are **randomly assigned** to a **control** group and a **treatment group**. - The **treatment** is the new change being tested in the experiment. - The **control group** is not exposed to the treatment. - The **treatment group** is exposed to the treatment. - The difference in metric values between the two groups measures the treatment’s effect on the test subjects.

Question 37

A/B test: Sampling

Answer 37

Random selection helps you create a representative sample that reflects the characteristics of the overall user population. - choose a appropriate **sample size**for your A/B test. - The larger the sample size = more precise the results, and the more likely you’ll get results that are **statistically significant** when there is a **difference between** group A and group B. - However, can be **expensive and time-consuming**.

Question 38

A/B test: Hypothesis testing

Answer 38

- **H**0: There is no difference in average revenue per user between A and B - **H**a: There is a difference in average revenue per user between A and B

Question 39

Experimental Design

Answer 39

refers to planning an experiment in order to collect data to answer your research question.

Question 40

Experimental Design Steps

Answer 40

1. Define your variables 2. Formulate your hypothesis 3. Assign test subjects to treatment and control groups

Question 41

Experimental Design: Define your variables

Answer 41

defining the independent and dependent variables example - **independent variable** is the medicine—the cause you want to investigate. - *dependent variable** is recovery time—the effect you want to measure.

Question 42

independent variable

Answer 42

refers to the cause you’re interested in investigating. A researcher changes or controls the independent variable to determine how it affects the dependent variable.

Question 43

dependent variable

Answer 43

refers to the effect you’re interested in measuring. “Dependent” means its value is influenced by the independent variable.

Question 44

Experimental Design: Formulate your hypothesis

Answer 44

- H0 is that the medicine has **no effect.** - Ha is that the medicine **is effective.**

Question 45

Experimental Design: Assign test subjects to treatment and control groups

Answer 45

In a **randomized controlled experiment**, test subjects are **randomly assigned** to a **control** group and a **treatment group**. - The **treatment** is the new change being tested in the experiment. - The **control group** is not exposed to the treatment. - The **treatment group** is exposed to the treatment. - The difference in metric values between the two groups measures the treatment’s effect on the test subjects.

Question 46

Randomization

Answer 46

helps control the effect of other factors on the outcome of an experiment.

Question 47

2 methods of Randomization

Answer 47

1. completely randomized design 2. randomized block design

Question 48

completely randomized design

Answer 48

test subjects are assigned to treatment and control groups using a random process.

Question 49

completely randomized design CONs

Answer 49

1. Relatively**low accuracy** due to lack of restrictions which allows environmental variation (nuisance) to enter experimental error. 2. **Not** suited for** large numbers** of treatments because a relatively large amount of experimental material is needed which increases the variation.

Question 50

randomized block design

Answer 50

minimize the impact of known nuisance factors. - **Blocking** is the arranging of test **subjects in groups**, or blocks, that are similar to one another. - then **randomly assign** the subjects within each block to treatment and control groups.

Question 51

Hypothesis Test vs Chi-squared Test

Answer 51

hypothesis tests are used to see **significant differences among groups**. Chi-squared tests are used to determine whether one or more observed **categorical variables** follow expected distribution(s)

Question 52

Chi-squared tests

Answer 52

used to determine whether one or more observed categorical variables follow expected distribution(s).

Question 53

2 main Chi-Squared Tests

Answer 53

1. Goodness of Fit 2. Test for Independence

Question 54

Chi-squared tests: Goodness of fit versus independence

Answer 54

is a hypothesis test that determines whether an observed **categorical variable follows an expected distribution.** H0: The week you observed follows your boss’s expectations that the number of website visitors is equal on any given day Ha: The week you observed does not follow your boss’s expectations; therefore, the number of website visitors is not equal across the days of the week

Question 55

Chi-Squared Tests Steps

Answer 55

1. Identify the Null and Alternative Hypotheses 2. Calculate the chi-square test statistic (X2) 3. Calculate the p-value 4. Make a conclusion

Question 56

The Chi-Squared Test for Independence

Answer 56

is a hypothesis test that determines whether or not **two categorical variables are associated**with each other. H0: The type of device a website visitor uses to visit the website is independent of the visitor’s membership status. Ha: The type of device a website visitor uses to visit the website is not independent of the visitor’s membership status.

Question 57

ANOVA testing

Answer 57

statistical technique used to check if the means of two or more groups are significantly different from each other - compares **continuous** variables with **categorical** variables can be **applied to the results** we get from a **linear regression**.

Question 58

Regression & ANOVA Relationship

Answer 58

Regression: IF and by HOW MUCH variables impact an outcome variable ANOVA: Pairwise comparisions. Understance nuance among elements that fueld regression analysis

Question 59

One-way ANOVA

Answer 59

Compares the means of **one continuous dependent variable** based on three or more groups of **one categorical variable**.

Question 60

Two-way ANOVA

Answer 60

Compares the means of **one continuous dependent variable** based on three or more groups of **two categorical variables**.

Question 61

Post hoc test:

Answer 61

Performs a pairwise comparison between all available groups while controlling for the error rate. - If we run **multiple hypothesis tests** all with a 95% confidence level, there is an **increasing chance** of a **false positive**. - The **post hoc test** will control for this, and allows us to run **many hypothesis tests** while **remaining confident with the accuracy** of the results.

Question 62

ANOVA vs Post-hoc results

Answer 62

Since the p-value is very small and we ANOVA tells us we can reject the null hypothesis that the mean price is the same for all diamond color grades but it doesnt specify which color and which price is different. post hoc test is useful because the one-way ANOVA does not tell us which colors are associated with different prices. The post hoc test will give us more information.

Question 63

One-way ANOVA

Answer 63

1. Build a simple linear regression model 2. Check the results 3. Run one-way ANOVA

Question 64

ANCOVA

Answer 64

is a statistical technique that test the difference of means between three or more groups while controlling for the effects of covariance.

Question 65

Covariates

Answer 65

- Covariates are the variables that are not of direct interest to the question we are trying to address. - By taking the covariates into account, we can **better isolate** the relationship between the categorical variable we are interested in and the Y variable. - This allows us to draw more accurate conclusions about the relationships among the variables.

Question 66

MANOVA

Answer 66

- manova or multi variant analysis of variance - that compares how two, or more continuous outcome variables, vary according to categorical independent variables. The independent variable must be **categorical** and the outcome variables must be **continuous**