Basics of Hypothesis Testing in Power BI

 Basics of Hypothesis Testing in Power BI

Introduction

Hypothesis testing is a fundamental statistical method used to make decisions or inferences about population parameters based on sample data. It helps answer questions like:

• Is a new marketing campaign increasing sales?

• Is the average salary of employees more than ₹50,000?

• Do two different regions perform equally in terms of revenue?

Concept	Explanation

Population

Entire group of interest (e.g., all students in India)

Sample

A part of the population selected for analysis

Hypothesis

A statement about a population parameter (e.g., average, proportion)

Test Statistic

A standardized value used to decide whether to reject the null hypothesis

P-value

Probability of observing your result if the null hypothesis is true

Significance Level (α)

Threshold for decision-making (commonly 0.05)

Types of Hypotheses

1. Null Hypothesis (H₀)

• The assumption that there is no effect or no difference.

• It is always tested with the aim of rejecting it.

• Example:

• “There is no difference in average sales between North and South.”

• “The average customer satisfaction score is 4.0.”

2. Alternative Hypothesis (H₁ or Ha)

• The assumption that there is an effect, or a difference exists.

• It challenges the null.

• Example:

• “The average customer satisfaction score is not 4.0.”

• “North region sales are significantly different from South.”

Step 1: Define Hypotheses

Clearly state H₀ and H₁.

🔸 Example:

• H₀: μ = ₹50,000

• H₁: μ ≠ ₹50,000

Step 2: Set Significance Level (α)

Common choices are:

• 0.05 (5% chance of error)

• 0.01 (1% chance of error)

Step 3: Choose the Test Type

Based on data and assumptions:

Condition	Test
Sample size < 30 and population SD unknown	T-Test
Sample size ≥ 30 and population SD known	Z-Test
Comparing means of two groups	Two-sample T-Test
Comparing proportions	Z-Test for proportions

Step 5: Find the Critical Value / P-value

• Compare calculated T or Z value to the critical value from tables

• OR use P-value approach:

• If P-value < α → Reject H₀

• If P-value ≥ α → Fail to reject H₀

Step 6: Make a Decision

• If test statistic lies in rejection region → Reject H₀

• Else → Fail to Reject H₀

Step 7: Draw Conclusion

Interpret in context of the problem:

“There is enough evidence to suggest that the average sales are different from ₹50,000.”

Power BI Step-by-Step Instructions 

Dataset : Salesdata

Sample Size = 30

Used for: One Sample T-Test
Hypothesis:

• H₀: Mean Sales = ₹50,000

• H₁: Mean Sales ≠ ₹50,000

1. Load Data into Power BI

• Open Power BI Desktop

• Click Home > Get Data > Excel

• Browse and select SalesData.xlsx

• Load the SalesData table

2. Create DAX Measures for Analysis

Go to Modeling > New Measure and create these one-by-one:

1. Mean Sales

Dax: 

Mean_Sales = AVERAGE(SalesData[SalesAmount])

2. Standard Deviation

Dax:

StdDev_Sales = STDEV.S(SalesData[SalesAmount])

3. Sample Size

Dax: 

Sample_Size = COUNT(SalesData[SalesAmount])

4. T-Statistic (assuming population mean = 50000)

Dax:

T_Value = 

VAR xBar = [Mean_Sales]

VAR mu = 50000

VAR s = [Sample_Size]

VAR n = [Sample_Size]

RETURN

    DIVIDE(xBar - mu, s / SQRT(n))

Following is Mathematical Formula for
One-Sample T-Test Formula

Where:

Meaning of Symbols

Symbol	Meaning
$\bar{X}$	Sample Mean (Average of the collected sample data)
$\mu$	Population Mean (Hypothesized mean under the Null Hypothesis $H_0$)
$s$	Sample Standard Deviation
$n$	Sample Size (Number of observations in the sample)
$t$	Test Statistic (Calculated t-value used for hypothesis test

5. T-Critical Value (for α = 0.05, two-tailed)

Dax:

T_Critical = T.INV(0.975, [Sample_Size] - 1)

6. Hypothesis Result

Dax: 

Test_Result = 

VAR t_stat = ABS([T_Value])

VAR t_crit = [T_Critical]

RETURN

    IF(t_stat > t_crit, "Reject Null Hypothesis", "Fail to Reject Null Hypothesis")

3. Build Power BI Visuals

Switch to Report View:

➤ Use Card Visuals for:

• Mean_Sales

• StdDev_Sales

• Sample_Size

• T_Value

• T_Critical

• Test_Result

Use Bar Chart to show average sales by region:

• X-axis: Region

• Y-axis: Average of SalesAmount

4. Interpret Results

Based on the dashboard:

• If |T_Value| > T_Critical, you reject the null hypothesis

• If not, you fail to reject it

Explain:

“If T_Value is 2.1 and T_Critical is 2.045, we reject H₀, and conclude average sales are statistically different from ₹50,000.”

Real world Problems and how to define the hypothesis

1. Student Average Marks Example

Problem:
A college claims that the average marks of students in statistics is 70.

Null Hypothesis (H₀):
The average marks of students is 70.

$$H_0: \mu = 70$$

Alternate Hypothesis (H₁):
The average marks of students is not equal to 70.

$$H_1: \mu \neq 70$$

Explanation for students:

• H₀ assumes the college claim is true.

• H₁ checks whether the claim is different from reality.

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2. Mobile Usage by Students

Problem:
A researcher claims that students spend more than 4 hours daily on mobile phones.

Null Hypothesis (H₀):
Students spend 4 hours or less on mobile phones.

$$H_0: \mu \le 4$$

Alternate Hypothesis (H₁):
Students spend more than 4 hours on mobile phones.

$$H_1: \mu > 4$$

Explanation:

• H₀ assumes normal or expected usage.

• H₁ tests whether usage is actually higher.

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3. Online Learning Effectiveness

Problem:
A teacher believes that online learning improves student performance.

Null Hypothesis (H₀):
Online learning does not improve student performance.

$$H_0: \mu_1 = \mu_2$$

Alternate Hypothesis (H₁):
Online learning improves student performance.

$$H_1: \mu_1 > \mu_2$$

Where

• $\mu_1$ = Average marks after online learning

• $\mu_2$ = Average marks before online learning

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✅ Simple way to explain to students

• Null Hypothesis (H₀) → Assumes no change / no effect / claim is true

• Alternate Hypothesis (H₁) → Assumes there is change / effect / difference