Achieving True Accuracy Using Statistics
A Statistical Analysis
Measuring Variables
Every engineer has always wanted to measure a parameter to assess the efficiency of their respective robots. This is very important to track many important things: improvement, efficiency, and etc. Measuring a single sample of data might seem adequate enough to calculate the TRUE value of the variable being measured. Sadly, this is not the case. A good statistician will tell you that the greater the number of samples, the greater the data given. This principle is important in finding a range in which the true value of your parameter lies in. Using a normal distribution and a confidence interval, you can find statistically significant results.
Confidence Intervals
To get the results we desire, we need to learn the process behind finding the true value. This process is called the Confidence Interval test. This test is instrumental to finding a range of values in which your true values lies in. This test, however, requires for your population — every sample possible — to have a normal distribution. Now what is a normal distribution? A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
No population has a perfect normal distribution, but they are really close. This begs the question: How do I know my population is normal? This question can be answered by 3 separate tests you have to do before you can find the true value for your variable.
Simple Random Sample
To asses if a population is normal, you have to randomly sample your variable. Simple Random Samples ensure that results obtained from your sample should approximate what would have been obtained if the entire population had been measured. To randomly pick samples, you can use many methods listed below.
Large Counts Condition
The second condition that we have to test for is the Large Counts Condition. This condition tests whether you have a large enough sample size compared to the population. For this, we have to see if our sample size exceeds 30. This is a standard created by the statistics community to properly asses a true values. This standard is known as the Central Limit Theorem.
10% Condition
The last condition we have to test is the 10 percent condition. This condition is tested to ensure independence in the samples. This independence helps us prove the population´s normality. To test this condition, we have to check if 10% of all samples are greater than our sample size. If this is true, then independence is proved.
Finding The True Value
When finding the true value, we have to make a crucial decision that affects the results we get. We have to choose if we value precision, accuracy, or both. Due to the inability to getting a PERFECT answer, we have to choose if we want to get a broad scope of answers and be very accurate, or to get a small scope of answers and be incorrect. This plays into the confidence level we choose. If we decide to choose a very high confidence level, we receive a broad interval which may not give much information; when we choose a very low confidence level, we receive a small scope of data which might not be accurate. To combat this, we choose a confidence level that fits our needs. For our example, we will choose a 95% confidence interval.
After choosing a confidence interval, you have to find a couple things that are essential to finding the true value: mean, standard deviation, sample size, and z-value. By utilizing resources such as excel or google sheets, we can these variables.
After finding the mean, z-score, and standard deviation, we can start plugging it into the formula above. For the z-score, you can utilize online tools to find the respective z-score for your confidence level. After plugging the variables into the formula, you receive an interval in which your true values exist.
Conclusion
Finding a true value is very instrumental to assessing values that may prove to be important. This process is not difficult with the use of the many online resources that exist nowadays. Omnicalculator — a calculator website — provides an easy way to calculate an interval. With all these different resources, there is no reason not to find a definite interval to provide people with accurate data.
