Dissertation Sample Size Stats Calculator

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Power Analysis & Sample Size Calculation Help

for Dissertation Students & Researchers

 

What is a Power Analysis?


     The purpose of a power analysis is to provide you with information needed to address your research question(s) in an accurate fashion. Power analysis is an important aspect of any quantitative study. Before going further it is important to define power. Power is broadly defined as the probability that a statistical significance test will reject the null hypothesis or the ability of a statistical test to detect an effect, given that the effect actually exists. Request Power Analysis Help Today
 

     Numerically, power is equal to 1-b (beta). In order to reject the null hypothesis (which states that there is no relationship between the variables of interest), power should be at least .80. In general, the larger your sample size, the greater the power.  Sometimes having too many subjects can decrease your power. Increasing sample size can also significantly increase your costs. A power analysis can help you decide in advance the amount of subjects needed to make your study worthwhile. We can help you conduct your power analysis to ensure you choose the appropriate statistical test(s) and effectively plan your data collection.

Learn More About Power Analysis

Let Us Help Conduct Your Power Analysis
 

     Given the importance of a power analysis, it is important that it is conducted properly and explained in simple language. In addition, if you are unsure about how to increase power, the effect size required for your study or differences between power value means, let us conduct your power analysis and explain the various components to you. If you are unsure what statistical test might be the most appropriate and powerful for your study, let us review your research question to help you choose the best statistical test for your study. Request Power Analysis Help Today

Power Analysis Examples

     Given the complexities of power analysis, we have created a few articles that provide examples of power analysis as it relates to different statistical analyses. Check out power analysis and sample size calculations for:

» Pearson Correlations
» T-Tests
» Multiple Regression
» Logistic Regression
» ANOVA
» MANCOVA
» Chi Square
     We realize these examples may not address all your power analysis questions and are ready to assist you with your specific dissertation needs.
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When conducting quantitative research, it is very important to determine the sample size for your study. Your sample needs to represent the target population you plan to examine. Sample size calculation should be done before you set off to collect any of your data. Almost all researchers generally like to work with large samples. However, this is not always feasible — especially for students (time, money, resources, etc.) — so it is a good idea to assess your need before any real research takes place to determine how many participants you really need (and can feasibly get) before planning your research.

This post presents a brief overview of sample size calculations and covers some of the basics. For complex cases and more detail, you will probably require more thorough text on the subject (see: Sample Size Determination and Power).

A Few Terms That Relate to the Size of Your Sample

Here are some expressions you will most likely come across when designing your study and deciding on a sample size.

  • Population – This is the complete set of data points, for example, all Americans.
  • Target population – This is the complete group for which you are studying; your data will have specific characteristics (demographics, clinical characteristics) that you are interested in — for example, Americans over the age of 65, who live at home and have had a stroke in the past 6 months.
  • Sample – A subset of the target population that represents the target population.
  • Margin of Error – The margin of error is about a degree of uncertainty in statistics. How much error will you allow? We would like the mean of our data to represent the mean of the target population; however, this is generally not going to happen. The margin of error tells us how much higher or lower than the true value will we let our sample mean fall. In articles, you usually see a +/-5% or +/-3% margin of error.
  • Confidence Interval – Confidence interval (CI) is usually set at 90%, 95% or 99%. It tells us how confident we are that if the study was repeated again and again, we would get the same results. If confidence level is 95%, we would get the same results in 95% of the cases.
  • Standard Deviation – Standard deviation tells us the variation in the data from your sample.
  • Power – This refers to the chance of missing a real difference (‘false negatives’). Usually, studies have a power of around 80%, which means that you accept the possibility that in 20% of the cases, the real difference was missed (you concluded there was no effect when there was one). Larger samples generally yield higher statistical power.

How to Calculate a Sample Size

It is fairly easy to determine your desired sample size. Formulas found in textbooks often appear very intimidating. However, they can be broken down and simplified if you are familiar with the above terms.

Scott Smith, Ph.D., presents a rather simpler version.  His formula for size calculation goes as follows:

(Z value)2 X standard deviation (1-standard deviation)/(margin of error)2 = n

This formula, however, can only be used for large populations or unknown population sizes.

The Z-value or Z-score corresponds with your chosen confidence level.  There are usually Z tables available that tell you the Z-score. You can then insert that value into the formula. Below are values for the most commonly used confidence intervals.

 

ClZ-value
90%1.645
95%1.96
99%2.58

You can use the formula to calculate a sample size for a confidence level of 99% and margin of error +/-1% (.01), using the standard deviation suggestion of .05.

(2.58)2*0.5(1-0.5)/(0.01)2 = 6.656*0.5(0.5)/0.0001= 16,641

The sample size for the chosen parameters should be 16,641, which is a very large sample. To make it a more realistic number, you might consider reducing your confidence level and margin of error. If you reduce it to 95% confidence level and 5% margin of error, you get a more manageable 384.16 participants, which you round up to 385.

Software for Calculating Your Sample Size

If this still appears like a pretty cumbersome task (or you have a smaller population size), you can also turn to various software programs and websites that will calculate the size for you. An example of such a site is The Survey System, which offers a free online sample size calculator. Another option is Survey Monkey’s sample size calculator, which can also be accessed online. These calculators usually ask you to enter your target population size, confidence level and margin of error.

You can also ask for guidance and assistance from other members of your department who might be more skilled at statistics. For additional ideas on how to get help with statistics, you can have a look at this post.

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