Does training really boost career growth?

Let's use data to measure its true impact, beyond just assumptions.

The Core Question for HR

Is there a statistically significant relationship between completing a specific training program and receiving a promotion within the next year?

We need to move from "we think it helps" to "we have evidence it helps". This is where the Chi-Square test comes in.

Start with What You Observed

First, we create a 'Contingency Table' with our actual employee data. These are the real-world numbers.

Here, we see that out of 70 trained employees, 50 got promoted. Is this difference significant or just random chance?

The Skeptic vs. The Believer

In statistics, we test two competing claims.

The goal of the Chi-Square test is to see if we have enough evidence to reject the skeptic's view (the Null Hypothesis).

Observed vs. Expected

Next, we calculate the values we would *expect* to see in each cell if there were no relationship (if the Null Hypothesis were true).

For 'Trained & Promoted': Expected = (70 × 80) / 150 = 37.3

The difference between Observed (O) and Expected (E) is the key to our test!

The Chi-Square Calculation

The Chi-Square formula measures the size of the difference between your observed and expected data.

For our data, the Chi-Square value is 19.33

Is the Relationship Significant?

A large Chi-Square value suggests the difference isn't due to chance. We compare it to a critical value (or find the p-value).

Conclusion: There is a proven, significant link between our training program and career promotion.

So What? Making Data Actionable

The analysis is done. Now, we act.