# Polaris’ Help Center: Statistical Tool for Calculating Statistical Differences in Survey Data Analysis As used in statistics, significant does not mean important or meaningful, as it does in everyday speech. Rather, a result is called “statistically significant” if it is unlikely to have occurred by chance. Significance is tested within the bounds of a given confidence level, usually 95 percent in most survey research.

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## Basic Statistical Testing for Significant Difference Between Two Proportions/Percentages

### Step 1:

desired confidence level: 99% 95% 90%

### Step 2:

 proportion 1: %
 proportion 2: %

### Step 3:

 sample size 1:
 sample size 2:
 <- check this box when group 2 is actually part of the larger sample

### Step 4:

population size: infinite actual/estimated
 Note: Choose ‘infinite’ when: N > (25 x n) or if you don’t know the actual size of the population. Rule of Thumb: Choose ‘infinite” when population is 1,000 or greater.

z =

see formula

## Basic Statistical Testing for Significant Difference Between Two Means

### Step 1:

Desired confidence level: 99% 95% 90%

### Step 2:

 Mean 1:
 Mean 2:

### Step 3:

 Standard deviation 1:
 Standard deviation 2:

### Step 4:

 Sample size 1:
 Sample size 2:

### Step 5:

Population size: infinite actual/estimated
 Note: Use ‘infinite’ when the group is larger than 1, or you don’t know the actual size of the overall population

t =

see formula

There are four important items you will need before you can calculate whether a survey result for one sample segment is significantly different than the rest of the population or another distinct segment. These include:

• Your chosen confidence interval (1)
• The size of the two sample segments you are testing (2)
• The estimated size of the population (3)
• The survey results for both segments that we’re testing (expressed either as a proportion or percentage or as a mean or average)

Note: If you are comparing means, you will also need to know the standard deviation of the mean for both segments.
Footnotes:
(1) The confidence interval, almost always in the range of 90 to 99 percent (most often 95%), is used to indicate the reliability of an estimate (in this case the margin of error). For example, a margin of error of +/- 5.0 percent at a 95 percent confidence level can be interpreted to mean that if you were to repeat the survey, 95 out of 100 times the results would come back with the same result within +/- 5.0 points.
(2) Along with the confidence level, the sample size determines the magnitude of the margin of error. A larger sample size produces a smaller margin of error, all else remaining equal.
(3) By population, we mean the larger body of people of interest that is too large to take a census. For example, the population of interest might be all females in Georgia between the ages of 25-50. As a rule of thumb, if a population is more than a couple of hundred people, we can consider it as “infinite” in size for the purpose of the calculator. The calculator can be adjusted for very small size populations (<150).