Achieving statistical validity is crucial for the reliability and accuracy of survey results. This guide covers the fundamental formulas and concepts for calculating statistical validity, margin of error, and estimating the necessary sample size for your surveys.

**Achieving Statistically Valid Survey Results**

Statistical validity is crucial for ensuring that your survey accurately reflects the opinions or behaviors of your target population. It's not just about the numbers; it's about how reliably those numbers speak for your entire group of interest. Several key factors contribute to achieving statistical validity:

**Representative Sampling:**Your survey sample should represent the population you're studying. This means the characteristics of your sample group (like age, gender, location) should closely match those of the larger population.**Accurate Data Collection:**The way you collect responses should minimize errors. This includes clear question wording, reliable data collection methods, and ensuring respondents understand and answer questions truthfully.**Avoiding Bias:**It's important to avoid any bias in how you select your sample or phrase your questions. Bias can skew results and reduce the validity of your survey.**Appropriate Survey Design:**The structure and content of your survey should be designed to effectively gather the information you need without leading or confusing respondents.

Now, how do these factors relate to the margin of error and sample size?

**Margin of Error:**This is about how much you can expect your survey results to differ from the real views of the entire population. A smaller margin of error means your results are more likely to mirror the true feelings or behaviors of the whole group you're studying.**Sample Size:**The number of people you survey (sample size) directly impacts your survey's validity. A larger sample size can provide more accurate and reliable results, reducing the margin of error. The sample size formula helps you determine the right number of respondents to ensure your survey results are dependable.

Both the margin of error and the appropriate sample size are integral to achieving statistical validity. They help ensure that your survey results are an accurate reflection of your target population's opinions or behaviors.

**Calculating Margin of Error**

The margin of error helps us understand how accurate our survey results are. It gives us a range that shows where the real answer likely falls.

For example, if we say that 60% of people like a certain proposed park plan, with a margin of error of 5%, the real percentage of people who like the movie could be as low as 55% or as high as 65%. *This range helps us be more confident in our assessment of public opinion.*

**Formula:**Where:

**Z**is the Z-score (we recommend 1.96 for 95% confidence level, see Choosing a Z-score)is the sample proportion (decimal, we recommend 0.50)*p*is the sample size*n*

**Example:** For a survey with 95% confidence level (Z=1.96), where 50% of the respondents (p=0.50) choose a particular option in a sample of 400 people (n=400), the margin of error is calculated as follows:

**Choosing a Z-score**

We generally recommend a 95% confidence interval, but if you desire a higher or lower degree of confidence, the following Z-scores can be used for each confidence interval:

**90%**β Z Score = 1.645**95%**β Z Score = 1.96**99%**β Z Score = 2.576

**Calculating your needed Sample Size**

### Option A: deriving sample from a known population size

The formula for calculating sample size with a known population incorporates the following:

**Formula:**Where:

*n*= Adjusted sample size for finite population*N*= Total population size"Sample size for infinite population" is calculated using Option B below:

### Option B: when you don't know your population size

This formula can be used when it is impractical to calculate your project area population (see calculating target population), or when the population is very large, such as a statewide survey.

This formula helps us understand how big our group of survey participants needs to be so that we can trust the results to reflect what most people think.

**Formula:**Where:

is the sample size*n*is the Z-score (1.96 for 95% confidence level, see Choosing a Z-score)*Z*is the margin of error*E*is the estimated proportion (if unknown, use p=0.5 for maximum sample size)*p*

**Example:** To achieve a margin of error of 5% (E=0.05) at a 95% confidence level, the required sample size would be 384 participants:

**Conclusion:** Understanding and correctly applying these formulas is key to ensuring the reliability and accuracy of your survey results. Accurate calculations of margin of error and sample size are essential components of statistical validity, enabling you to draw meaningful conclusions from your survey data.

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