Understanding Confidence Intervals and MOE in Statistics

Research Fundamentals #6

This lesson builds upon our understanding of Sample Size and Power Analysis. If you haven’t reviewed those concepts yet, go back and do so first—each step in this series follows a structured learning approach.

What Are Confidence Intervals?

A Confidence Interval (CI) is a range of values that likely contains the true number in a range (parameter). Instead of providing a single estimate (mean). The CI provides a range that reflects the uncertainty in statistical estimation.
-Dr. Santangelo
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Example someone scores a 104 on an IQ test we may say there true IQ falls between 98-108. We then may make a statement we are 95% confident the individual’s true IQ score is somewhere in the range between 98-108.

Key Points

95% Confidence Interval means that if we repeated the study multiple times, 95% of the intervals calculated contain the true parameter. Wider intervals indicate more uncertainty, while narrower intervals suggest more precise estimates. Confidence intervals are preferred over point estimates because they convey the degree of uncertainty in data.
–Dr. Santangelo
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Example
A study estimates the average height of adults to be 170 cm with a 95% CI of 167 cm to 173 cm. This means we are 95% confident that the true average height falls within this range.

The Role of Margin of Error (MOE)

The Margin of Error (MOE) is a means to quantify the uncertainty in an estimate, representing half the width of the confidence interval.
-Dr. Santangelo
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Key Factors Affecting MOE

Sample Size: A larger sample decreases the margin of error.
Variability in Data: More variation increases ▲the margin of error.
Confidence Level: Higher confidence (e.g., 99%) results in a larger MOE.

Interpreting Confidence Intervals in Research

Formula

Z= Z-score corresponding to your confidence level (e.g., 1.96 for a 95% confidence level),
σ= standard deviation
n= sample size.

Common Misinterpretations *Avoid*
Incorrect “There is a 95% probability that the true value is in the interval. (Incorrect)
correct “If we repeat the study multiple times, 95% of the calculated intervals will contain the true parameter. (Correct)

Key Takeaways

Confidence Intervals provide a range of plausible estimates, unlike single values.
Margin of Error quantifies uncertainty and decreases with larger sample sizes. Higher confidence levels lead to wider intervals, balancing certainty and precision.
Interpreting CI correctly avoids common statistical misinterpretations.

Next Lesson: Effect Size and Practical Significance

In the next lesson, we will explore effect size, why it matters, and how it helps determine the practical significance of research findings.