The confidence interval is an important measure of describing quantitative data. According to Rees (2015), confidence interval helps to establish the accuracy of population measures. Basically, the confidence interval identifies the range of values that form part of parameter measure like the mean. Confidence intervals are calculated for continuous variables. The continuous variables in this refers to quantitative measures that can take any value between the maximum and minimum figures, for example, age, BMI, income, and blood pressure among others. Confidence intervals are important in ascertaining the accuracy of statistical measures describing continuous variables, thus it is important to outline the procedure for calculating the interval level.
Foremost, it is important to highlight the type of variables required to calculate confidence intervals for continuous variables. Foremost is the population mean, which refers to the average of the total value of the continuous variable ( Kelley, & Pornprasertmanit,2016) . Secondly is the second deviation, which measures how far variables are spread around the population mean. Thirdly is the number of variables in the population. Lastly is the Z score, which is a variable calculated for each confidence interval that ranges between 0-100%. Therefore, the process of calculating the confidence interval begins with the calculation of the four variables specified above and inputting the values into a formula to get the results as described above.
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Step 1: Calculate the number of observations of the continuous variable that is donated by the symbol n.
Step 2: Calculate the mean of the population’s standard
The mean value I calculated by adding up the controllable variables and dividing the total by the number of the total observation. For example, the mean age of 50 students between 9-19 years would be calculated by summing together each boys age, and dividing this amount by 50.
Arithmetic Mean (X) = (r1 +r2 +r3 +r4)/n
Where r= variables
N= number of observations
Step 3: Calculate the standard deviation of the continuous variable.
The formula for the standard deviation is
Standard deviation (δ )=√ ∑(X1-X) 2 /n-1
Where
X=Mea
X1= Variables
N= number of observations
Step 4: Compute the standard error (SE) of the population
Basically, the standard error is the standard deviation divided by the square root of the number of observations as shown in the formula below ( Kelley, & Pornprasertmanit,2016).
SE = δ/√n
Step 5: Compute the critical value
Computing the critical value is arguably one of the most important but challenging task during the formulation of the confidence interval. The critical value is usually developed for the required confidence interval. There are three major steps in calculating the critical value.
Calculate the alpha
Alpha measures the probability that the population dies not fall within the confidence interval region.
α=1-Confidence interval
Calculate the critical probability
P= 1-α/2
Determine the degrees of freedom by adjusting the number of observations with one
Degrees of freedom=n-1
Use the critical value table to pock the value that is by running the degrees of freedom against the critical probability. For a small sample that is greater than 30, the t-table should be used. On the other hand, the z-table should be used for bigger samples greater than 30.
Use the critical value to calculate the margin of error (ME)
Margin of Error= Critical value * Standard error
Calculate the confidence interval
Confidence interval= Mean (sample statistic) + ME
The confidence interval is expressed in terms of the maximum value that is positive and minimum value that is negative in nature. This is the last step of calculating the confidence interval of a continuous variable.
References
Kelley, K., & Pornprasertmanit, S. (2016). Confidence intervals for population reliability coefficients: Evaluation of methods, recommendations, and software for composite measures. Psychological Methods , 21 (1), 69.
Rees, D. G. (2018). Essential statistics . Chapman and Hall/CRC.
