Introduction to Hypothesis Testing - The Weather Edition ???

Welcome back, fellow data sleuths! Let's add some technical meat to our Hypothesis Testing stew, focusing on our Berlin winter weather case. ???♂???

Null and Alternative Hypotheses (H0 and Ha) Explained ?????

First, let's define these terms:

• H0 (Null Hypothesis): This is the default assumption, suggesting no effect or no difference. It's what we try to disprove.
• Ha (Alternative Hypothesis): This is what you propose against H0, indicating a potential effect or difference.

Example:

• H0: "Berlin's winter and summer temperatures are the same."
• Ha: "Berlin's winter temperatures are colder than summer."

Significance Level (α) - Setting the Bet ??

Is there a formula for α? Not exactly.

α is more of a choice reflecting how much risk of error you're willing to accept.

It's about balancing false positives and missed truths.

Example:

• We chose α = 0.05.
• No complex formula, just a commonly accepted risk threshold in many fields.

Type I and II Errors - Avoiding Mistakes ??

Type I Error (False Positive):

1. Definition: A Type I error occurs when a null hypothesis that is actually true is rejected. In other words, it is the error of concluding that there is a significant effect or difference when there is no such effect or difference in reality.
2. Symbol: α (alpha), Type I error is the predetermined level of risk that researchers are willing to take when conducting a hypothesis test. Commonly chosen levels include 0.05 or 0.01.Type I Error Examples:

• In our case concluding that Berlin's winter temperatures are colder than summer when they are not.
• Declaring a new drug is effective when they are not.
• Concluding a marketing campaign increased sales when it didn't.
• Believing a new teaching method improves test scores, but it doesn't.

Type II Error (False Negative):

1. Definition: A Type II error occurs when a null hypothesis that is actually false is not rejected. It is the error of failing to detect a significant effect or difference when such an effect or difference exists in reality.
2. Symbol: β (beta), the probability of a Type II error is influenced by factors like sample size, effect size, and the chosen significance level (α).

Type II Error Examples:

• Failing to conclude that Berlin's winter temperatures are colder than summer when they are significantly colder or even freezing.
• Missing the effectiveness of a new drug because of insufficient evidence.
• Overlooking the real impact of a marketing campaign on sales.
• Failing to recognize the benefits of a new teaching method on student learning.

P-Values: Cracking the Code - Definition, Calculation, Example ??

Definition:

The p-value measures the probability of obtaining the observed results, or more extreme if H0 is true. It's about assessing the evidence against H0.

How to Find P-Value:

• Collect your data.
• Choose the right statistical test (like a t-test, or chi-square) [I will detail out these two in separate articles]
• Perform the test to get the test statistic.
• Use this statistic to find the p-value from statistical tables or software.

Calculating P-Value with Weather Data:

Let's say we have temperature data for Berlin's summers and winters. We perform a t-test and get a test statistic. Consulting a t-distribution table or software, we find our p-value to be 0.03.

Using the P-Value:

• Since [p < α] or 0.03 < 0.05 (our α), we reject H0, supporting the claim that Berlin's winters are colder than summers.

Wrap-Up with Technical Flair ?????

We've now added a layer of technical understanding to our weather-based exploration of Hypothesis Testing.

Remember, it's not just about the conclusion; it's about how rigorously and thoughtfully we arrive there.

In the next blog, we'll explore what is a t-test, chi-square test ?????

#datawisdom #technicaldeepdive #hypothesistesting