# Statistical calculators

Make common statistical calculations in a simple way

## Sample calculator for proportions

Calculate the sample size you need when your survey measures a proportion or a percentage (for instance, % of smokers in a population). Using this advanced calculator you will see how error margin, confidence level and sample size are interrelated. More information about the used formulas here.

To use the calculator:

• Enter the size of the universe and the degree of heterogeneity of the population.
• Enter 2 out of the 3 remaining parameters. For instance, if you indicate the sample size and the confidence, margin of error will be calculated.
• Press ‘Calculate’’. The resultant value will be highlighted.

Size of the universe

Number of individuals that make up the population under study.

Heterogeneity %

Degree of diversity of the universe. Tipically we use 50%, the worst case.

Margin of error %

A smaller margin of error requires a larger sample size.

Confidence level %

A larger confidence level requires a larger sample size. Normally (80%-99%).

Sample size

Individuals to be surveyed

If you survey people, the real data you are looking for will be the of the times in the interval in relation to the data you observe in the survey.

## Sample calculator for means

Calculate the sample size you need when your survey measures an average value (for example, the average number of cigarettes smoked per individual in the population). In this advanced calculator you will be able to see how margin of error, confidence level and sample size are interrelated. More information about the used formulas here.

To use the calculator:

• Enter the size of the universe and the approximate variance that you expect for your data.
• Enter 2 out of the 3 remaining parameters. For instance, if you indicate the sample size and the confidence level, margin of error will be calculated.
• Press ‘Calculate’. The resultant value will be highlighted.

Size of the universe

Number of individuals that make up the population under study.

Heterogenity %

Degree of diversity of the universe. Tipically we use 50%, the worst case.

Margin of error

A smaller margin of error requires a larger sample size.

Confidence level %

A larger confidence level requires a larger sample size. Normally (80%-99%).

Sample size

Individuals to be surveyed.

If you survey people, the real data you are looking for will be the of the times in the interval in relation to the data you observe in the survey.

## Significant difference calculator between proportions

To use the calculator:

• Enter the sample size and the observed % for the sample 1.
• Do the same with sample 2.
• Enter which confidence level you want in order to prove that the observed difference is not by chance. A larger confidence level requires a larger observed difference.
• ...so there it is! Result is re-calculated each time you modify the different parameters. The calculator evaluates if the difference is significant and which is the minimum difference you have to observe to get this significance.

Sample 1

People from the group 1 who answered the question

Percentage 1 %

Observed result of the Group 1

Sample 2

People from the group 2 who answered the question

Percentage 2 %

Observed result of the Group 2

Confidence level %

Confidence level over the significance you want to get

Is this difference significant?
The minimum difference to state with a confidence of 95% it is significant is: is: %

## Significant difference calculator between means

Check if the observed difference between two samples is significant regarding an average value. For example, you want to know if mothers from the country A have more children on average than mothers in country B. After surveying 1.000 mums from each country you get that mothers from country A have 2,4 children on average and mothers from country B a 3,1. How you can determine if the difference is due to sample size effects or it is real? By doing a significant test. You have more information in the following post.

To use the calculator:

• Enter the sample size, the observed mean and standard deviation for the sample 1.
• Enter which confidence level you want in order to prove that the observed difference is not by chance. A larger confidence level requires a larger observed difference.
• ...so there it is! Result is re-calculated each time you modify the different parameters. The calculator evaluates if the difference is significant and which is the minimum difference you have to observe to get this significance.

Mean 1

Observed mean in group 1.

Mean 2

Observed mean in group 2.

Sample Size 1

People from the group 1 who answered the question.

Sample Size 2

People from the group 2 who answered the question.

Standard deviation 1

Standard deviation observed in group 1.

Standard deviation 2

Standard deviation observed in group 2.

Mean 2 %

Observed mean in group 2.

Is this difference significant?

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