6. Hypothesis Testing

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In hypothesis testing, what are we looking for?

A statistically significant difference between two measurements

What is the purpose of testing the hypothesis that a coin is fair?

To determine if there is a statistically significant difference in the number of heads and tails

If a fair coin is flipped 100 times and comes up heads 52 times and tails 48 times, is this a statistically significant difference?

No, it is not statistically significant

If a fair coin is flipped 100 times and comes up heads 32 times and tails 68 times, is this a statistically significant difference?

Yes, it is statistically significant

In hypothesis testing, what is the null hypothesis typically denoted as?

H0

What does the alternative hypothesis represent in hypothesis testing?

Yes, there is a difference between population A and population B

What is the purpose of A/B testing?

To determine which version has the most impact in meeting business goals

What does the 'A' typically refer to in A/B testing?

Control

What is the focus of A/B testing?

Statistically significant improvements in measured data

What is the primary goal of A/B testing?

To determine a 'winner' and a 'loser' based on statistically significant improvements

In A/B testing, what does the 'B' typically refer to?

Variation

What does the determination that color makes a difference in sales confirm?

The alternative hypothesis

What are the two mutually exclusive hypotheses in hypothesis testing?

Null hypothesis and alternative hypothesis

What do hypothesis tests aim to determine?

Which hypothesis—the null or the alternative—is the true one

What is the alternative hypothesis commonly referred to as?

The alternative hypothesis

Which hypothesis is typically referred to as the null hypothesis?

H0

What sets the degree of variance around the calculated value that stakeholders are willing to tolerate?

Alpha value

What motivates the formation of hypotheses in marketing analysis?

Evaluation questions

What do evaluation questions in marketing analysis often reduce to?

Questions of difference

What are the null hypothesis and the alternative hypothesis used to evaluate?

Presence of a difference

What is the formula for calculating a confidence interval in Excel or Google Sheets based on?

Alpha value, sample size, and standard deviation

What addresses questions of difference in marketing analysis?

Hypotheses

What is the percentage of the confidence interval determined by?

Alpha value

What are hypotheses in marketing analysis tested through?

Data analysis

What do evaluation questions in marketing analysis often reduce to?

Simple question of whether there is a difference

What are confidence intervals based on?

Probabilities and sample sizes

What involves the formation of hypotheses in marketing analysis?

Addressing questions about differences and effects

What does hypothesis testing involve?

Null hypothesis and alternative hypothesis

What does a low p-value indicate?

A low probability of chance and a high probability of statistical significance

What is the purpose of the alpha value in statistical analysis?

To set the boundary for acceptable p-values in an analysis

What is the standard assumption for the alpha value in statistical analysis?

$\alpha = 0.05$

What does a lower alpha value indicate in statistical analysis?

Higher confidence in the analysis

What do confidence intervals establish in statistical analysis?

A range of precision for calculated values

What does a 95% confidence interval for a fair coin indicate?

A 95% confidence that the observed outcome will fall within the interval

What is the probability represented by a p-value of 0.04?

4%

What is the T-test method used for in statistical analysis?

Calculating a p-value

What does a statistically significant difference in data indicate?

An effect worthy of further investigation

What does the P-value represent in statistical analysis?

The probability that a difference between two data measurements is due to random chance

What is the purpose of a 95% confidence interval for a fair coin in statistical analysis?

To establish a range of precision for the expected outcomes

What is the acceptable p-value determined by in statistical analysis?

The alpha value

What is a 'false positive' in the context of testing a hypothesis?

When data seems to confirm something is true, but it is false

What is the main reason for the possibility of errors in statistical analyses?

Statistical analyses are ultimately based on probability

What is the consequence of not conforming to ideal conditions like perfect randomization in statistical analyses?

A small chance of errors in determining the hypothesis from the data

What is the key factor leading to errors in determining a hypothesis from marketing data?

Statistical analyses are based on educated predictions and probability

What is a Type I error in hypothesis testing?

Rejecting the null hypothesis when it is true

What is a Type II error in hypothesis testing?

Accepting the null hypothesis when it is false

In hypothesis testing, what is the null hypothesis typically referred to as?

H0

In hypothesis testing, what is the alternative hypothesis typically referred to as?

H1

What is the focus of Type I error in hypothesis testing?

False positive

What is the focus of Type II error in hypothesis testing?

False negative

What does a Type I error lead to in hypothesis testing?

Incorrectly concluding a difference when there isn't one

What does a Type II error lead to in hypothesis testing?

Incorrectly concluding no difference when there is one

What is the first hypothesis typically referred to as in hypothesis testing?

Null hypothesis (H0)

What is the second hypothesis typically referred to as in hypothesis testing?

Alternative hypothesis (H1)

What is the error referred to as when the null hypothesis is mistakenly rejected and the alternative hypothesis is accepted?

Type I error

What is the error referred to as when the null hypothesis is mistakenly accepted and the alternative hypothesis is rejected?

Type II error

Study Notes

Confidence Intervals and Hypothesis Testing in Marketing Analysis

  • Confidence intervals are based on probabilities and sample sizes and can be calculated for any degree of confidence, not just 95%.
  • The alpha value (𝛂) sets the degree of variance around the calculated value that stakeholders are willing to tolerate.
  • The percentage of the confidence interval is determined by the alpha value, e.g., a 95% confidence interval is based on a 5% alpha value (𝛂 = 0.05).
  • The formula for calculating a confidence interval in Excel or Google Sheets includes the alpha value, sample size, and standard deviation.
  • An example calculation of a 95% confidence interval for weekly sales data in a spreadsheet is provided, showing a range of likely sales values.
  • Hypotheses are proposed answers to evaluation questions in marketing analysis and are tested through data analysis.
  • Evaluation questions in marketing analysis motivate the formation of hypotheses, such as whether website color affects sales.
  • Evaluation questions often boil down to a question of difference, such as differences between demographic groups in purchasing behavior or the cost-effectiveness of advertising.
  • Hypotheses address questions of difference, like whether there is a difference in sales between different website colors.
  • Hypothesis testing involves the null hypothesis (H0) and the alternative hypothesis (H1) which are used to evaluate the presence of a difference.
  • Evaluation questions in marketing analysis often reduce to the simple question of whether there is a difference, such as differences in purchasing behavior or campaign effectiveness.
  • The formation of hypotheses and hypothesis testing are integral parts of marketing analysis, addressing questions about differences and effects.

Understanding P-Values, Alpha, and Confidence Intervals

  • A statistically significant difference in data can indicate an unfair coin or an effect worthy of further investigation.
  • P-value represents the probability that a difference between two data measurements is due to random chance.
  • P-value is usually calculated by software and expressed in decimal form.
  • A low p-value indicates a low probability of chance and a high probability of statistical significance.
  • The T-test method is one way to calculate a p-value.
  • A p-value of 0.04 means there is a 4% chance the measured difference occurred by chance.
  • The acceptable p-value is determined by the alpha value, which sets the boundary for acceptable p-values in an analysis.
  • A lower alpha value means higher confidence in the analysis.
  • A standard alpha assumption is 5% (𝛂 = 0.05) for acceptable significant difference.
  • Confidence intervals establish a range of precision for calculated values, giving a specific degree of confidence that observed results will match the calculation.
  • For a fair coin, the 95% confidence interval for flipping tails is 10 flips out of 100, meaning there's a 95% chance tails will come up within 10 flips of the statistical mean of 50 flips.
  • The 95% confidence interval for a fair coin indicates a 95% confidence that it will come up tails somewhere between 40 to 60 times.

Test your understanding of confidence intervals, hypothesis testing, p-values, and alpha values in marketing analysis with this quiz. Assess your knowledge of how these statistical concepts are applied in evaluating data, forming hypotheses, and making informed marketing decisions.

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