Correlation vs Causation in Player Performance

Business Context

PulsePlay, a mobile sports game, noticed that players who spend more time in training mode tend to win more ranked matches. The product team wants to know whether training time actually causes better performance, or whether the relationship is only correlational.

Problem Statement

You are given summary statistics from 200 players. First, quantify the observed association between weekly training hours and weekly ranked wins. Then assess whether this proves causation, especially after accounting for player skill level as a potential confounder.

Given Data

Metric	Value
Number of players	200
Correlation between training hours and ranked wins	0.42
Significance level	0.05
Mean training hours per week	6.8
SD of training hours	2.4
Mean ranked wins per week	15.2
SD of ranked wins	5.1
Simple regression slope: wins on training hours	0.89
Multiple regression slope after controlling for skill rating	0.18
Standard error of adjusted slope	0.11

Additional context	Top-skill players are more likely to use training mode

Requirements

Test whether the correlation between training hours and ranked wins is statistically different from 0.
Interpret the simple regression slope in business terms.
Test whether the adjusted training effect remains significant after controlling for skill rating.
Explain clearly why a statistically significant correlation does not imply causation.
State what additional analysis or experiment would be needed to make a causal claim.

Assumptions

Player observations are independent.
The correlation test uses the standard t-test for Pearson correlation.
The regression coefficient standard error is valid under standard linear model assumptions.
Skill rating is a plausible confounder because stronger players both train more and win more.

Business Context

Problem Statement

Given Data

Metric	Value
Number of players	200
Correlation between training hours and ranked wins	0.42
Significance level	0.05
Mean training hours per week	6.8
SD of training hours	2.4
Mean ranked wins per week	15.2
SD of ranked wins	5.1
Simple regression slope: wins on training hours	0.89
Multiple regression slope after controlling for skill rating	0.18
Standard error of adjusted slope	0.11

Additional context	Top-skill players are more likely to use training mode

Requirements

Test whether the correlation between training hours and ranked wins is statistically different from 0.
Interpret the simple regression slope in business terms.
Test whether the adjusted training effect remains significant after controlling for skill rating.
Explain clearly why a statistically significant correlation does not imply causation.
State what additional analysis or experiment would be needed to make a causal claim.

Assumptions

Player observations are independent.
The correlation test uses the standard t-test for Pearson correlation.
The regression coefficient standard error is valid under standard linear model assumptions.
Skill rating is a plausible confounder because stronger players both train more and win more.

Business Context

Problem Statement

Given Data

Metric	Value
Number of players	200
Correlation between training hours and ranked wins	0.42
Significance level	0.05
Mean training hours per week	6.8
SD of training hours	2.4
Mean ranked wins per week	15.2
SD of ranked wins	5.1
Simple regression slope: wins on training hours	0.89
Multiple regression slope after controlling for skill rating	0.18
Standard error of adjusted slope	0.11

Additional context	Top-skill players are more likely to use training mode

Requirements

Test whether the correlation between training hours and ranked wins is statistically different from 0.
Interpret the simple regression slope in business terms.
Test whether the adjusted training effect remains significant after controlling for skill rating.
Explain clearly why a statistically significant correlation does not imply causation.
State what additional analysis or experiment would be needed to make a causal claim.

Assumptions

Player observations are independent.
The correlation test uses the standard t-test for Pearson correlation.
The regression coefficient standard error is valid under standard linear model assumptions.
Skill rating is a plausible confounder because stronger players both train more and win more.

Business Context

Problem Statement

Given Data

Metric	Value
Number of players	200
Correlation between training hours and ranked wins	0.42
Significance level	0.05
Mean training hours per week	6.8
SD of training hours	2.4
Mean ranked wins per week	15.2
SD of ranked wins	5.1
Simple regression slope: wins on training hours	0.89
Multiple regression slope after controlling for skill rating	0.18
Standard error of adjusted slope	0.11

Additional context	Top-skill players are more likely to use training mode

Requirements

Test whether the correlation between training hours and ranked wins is statistically different from 0.
Interpret the simple regression slope in business terms.
Test whether the adjusted training effect remains significant after controlling for skill rating.
Explain clearly why a statistically significant correlation does not imply causation.
State what additional analysis or experiment would be needed to make a causal claim.

Assumptions

Player observations are independent.
The correlation test uses the standard t-test for Pearson correlation.
The regression coefficient standard error is valid under standard linear model assumptions.
Skill rating is a plausible confounder because stronger players both train more and win more.

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Given Data

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Correlation vs Causation in Player Performance

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Your Answer

Correlation vs Causation in Player Performance

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Correlation vs Causation in Player Performance

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Your Answer