Harmoni can calculate the margin of error in your analysis table or chart. The margin of error tells you how much your survey results could differ from the real population value at a specified confidence level.
In this article
1. Margin of Error
In Harmoni, the option to calculate the margin of error (MoE) is available in the modify menu.
The modify menu is available to Creators and Explorers. Viewers can also interact with these features when they have access to dashboards, or stories where the analysis can be zoomed.
Selecting the margin of error option adds the +/- error margin when percentages, sum percentages or averages are displayed in the analysis table.
Analysis Table
To add the margin of error, open the modify menu and click the MoE icon. The margin of error is added to each row in the analysis table, below the associated percentage or average. It shows you how much the percentage could be higher or lower compared to the results from your sample.
Visualize
You can add margin of error onto your chart if needed. After visualizing your chart, access the modify menu and click MoE.
Note: MoE is not available for stacked bar, plot or spider graphs.
2. Margin of Error Statistics
The margin of error tells you how many percentage points (or points when viewing averages) your results could differ from the real population value at a specified confidence level.
For example, at a confidence level of 95%, a 4% margin of error means that your survey value will be within 4 percentage points of the real population value 95% of the time.
Mathematically at a confidence level γ, a sample-sized n of a population having expected standard deviation σ has a margin of error:
moe(γ) = z(γ) sqrt(σ2/n)
Where:
- z(γ) denotes the quantile (also, commonly, a z-score), and
- sqrt(σ2/n) is the standard error.
For proportions (percentages) the standard error is sqrt(p*(1-p)/n).
For numeric measure values, the standard error depends on the standard deviation of the values.
To form a confidence interval for a population parameter, the margin of error is added to and subtracted from the point estimate (mean). The margin of error is, therefore, half of the width of a confidence interval.
Usually, a confidence level of 95% is used. If the confidence level is increased (e.g., to 99%), then the margin of error will increase. Conversely, a larger sample size gives a smaller margin of error.
Where to from here?
Learn more about statistics.