In cases where you’ve collected a lot of data about a specific population and you want to calculate the “best guess” parameter, this point estimate calculator proves extremely useful. It makes use of the different point estimate formulas to provide you with the most precise possible value. Apart from learning how to use this point estimate calculator, we’ll also learn how to find point estimate manually, and other relevant information.
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How to use the point estimate calculator?
This point estimate calculator is very useful, especially in finding point estimate statistics. The best thing about this online tool is that it’s very easy to use. If you need to find the most accurate point estimates, follow these steps:
- First of all, enter the value for the Number of Successes.
- Then enter the value for the Number of Trials.
- Finally, enter the value for the Confidence Interval which is a percentage value.
- These are the only values needed by this calculator to give you the point estimate statistics. After entering all of the required values, the calculator will generate a number of results including the Best Point Estimation, the Maximum Likelihood Estimation, the Laplace Estimation, Jeffrey’s Estimation, and the Wilson Estimation.
How do you calculate the point estimate?
For you to understand the concept of point estimate better, let’s use a simple example. Try to imagine that you’re tossing a coin. Each time you toss the coin, take note of the result. If you have an unbiased coin and you toss it several times, you should get a result of about 50% tails and 50% heads.
But what happens if your coin has a slight bias. For instance, what if it’s bent slightly? In such a case, you might discover after tossing the coin a lot, either the head or the tail appears more frequently. This shows that the slight bias changes the probability of getting either of the results for that specific coin.
The point estimate refers to the probability of getting one of the results. After you have tossed your biased coin for a certain number of times and you’ve collected enough data pertaining to the “behavior” of the coin, you can use that data when using the point estimate calculator.
Of course, you can also perform the calculations manually then check the results with the calculator. As you learn how to find point estimate, there are different point estimate formulas for you to use. These are the Maximum Likelihood Estimation formula or MLE, the Wilson Estimation formula, the Laplace Estimation formula, and the Jeffrey Estimation formula.
Using each of these formulas will provide you with results that differ slightly. Therefore, you must use these formulas in different situations too. The great thing about this calculator is that it selects the most relevant result for you automatically. Also, it provides you with the results for all the formulas. Going back to calculating the point estimate manually, follow these steps:
- First, you need to have the value for the number of successes. In the example we used, this refers to the number of tails you got after tossing the coin for a certain number of times.
- You should also have the value for the number of trials. In our example, this refers to the number of times you tossed the coin.
- Finally, you should also have the value for the confidence interval. This refers to the probability that you’ve made the best point estimate correctly and it’s within the margin of error.
- You also need to have the value of the z-score which comes from when you’ve calculated the confidence interval.
- Once you have all of the required values, you can use the formulas to calculate the point estimate. Here are the equations for the different formulas:
- for the Maximum Likelihood Estimation, the equation is MLE = S / T
- for the Laplace Estimation, the equation is Laplace = (S + 1) / (T + 2)
- for the Jeffrey Estimation, the equation is Jeffrey = (S + 0.5) / (T + 1)
- for the Wilson Estimation, the equation is Wilson = (S + z²/2) / (T + z²)
- After calculating all of the four values manually, you can check the accuracy of your calculation using the online calculator. Once you’ve verified that they’re all correct, you can select the most accurate value. Base your selection on these rules:
- If the value of the MLE ≤ 0.5, select the Wilson Estimation as this is the most accurate.
- If the value is 0.5 < MLE < 0.9, select the Maximum Likelihood Estimation as this is the most accurate.
- If the value is 0.9 < MLE, select the smaller value between the Laplace and Jeffrey Estimations as this is the most accurate.
How do you find the point estimate of the population mean?
In some cases, you need to determine the point estimate of a population mean. To illustrate this, let’s work with an example. Aside from determining the point estimate of the population mean, you also have to determine the margin of error when the lower bound of your confidence interval is 125.8 and the upper bound of your confidence interval is 152.6.
In the example, we’re given [125.8<=mu<=152.6]. Find the population mean using this formula:
[bar(x)-“error”<=mu<=bar(x)+”error”] where [bar(x)] is the point estimate for the mean.
Let’s input the values we already have into the formula:
[139.2-13.4<=mu<=139.2+13.4]
Therefore, the error is 13.4 and the point estimate for the population mean is 139.2.
What is a point estimate in statistics?
Using the simplest definition, any statistic can also be a point estimate. This is because a statistic serves as an estimator of a given parameter in a population. Consider these examples:
- A sample standard deviation “s” is the point estimate of a population standard deviation “σ.”
- A sample mean “x” is a point estimate of a population mean “μ.”
- A sample variance “s2” is a point estimate of a population variance “σ2.”
When you look at this in a more formal perspective, the occurrence of the estimate is a result of the application of the point estimate to a sample data set. The points are individual values compared to the interval estimates which are a set of values.
