stataimlCalculate Confidence Level from Z-score
Z-score is a standardized score which measures how many standard deviations a data point is from the mean of a given distribution.
Z-score can be 0 (data point is similar to the mean), positive (data point is greater than the mean), and negative (data point is lesser than the mean).
Z-score can be used for calculating the confidence level to find the range of values that is likely to contain the true mean of a population.
The following example explains how to find the confidence level from a given Z-score.
Example 1
We will use the pnorm function from R to calculate the confidence level from a given Z-score.
For example, if you have a Z-score of 1.96 and you want to find the confidence level that corresponds to a Z-score of 1.96.
First, let’s find the probability value for a Z-score of 1.96.
pnorm(1.96, lower.tail = FALSE)
# output
0.025
This is a one-sided probability value for a Z-score of 1.96. The two-sided probability value would be 0.05.
A probability value of 0.05 would give a confidence level of 95% (100-5=95).
It means that a Z-score of 1.96 corresponds to a 95% confidence interval.
This means that if you get an absolute Z-score greater than 1.96, it means you are 95% confident that the data point is significantly different (greater or lesser) than the population mean.
The Z-score greater than 1.96 also refers to p < 0.05 and leads to the rejection of the null hypothesis.
Example 2
For example, if you have a Z-score of 2.58 and you want to find the confidence level that corresponds to a Z-score of 2.58.
First, let’s find the probability value for a Z-score of 2.58
pnorm(2.58, lower.tail = FALSE)
# output
0.005
This is a one-sided probability value for a Z-score of 2.58. The two-sided probability value would be 0.01.
A probability value of 0.01 would give the confidence level of 99% (100-1=99).
It means that Z-score of 2.58 corresponds to 99% confidence interval.
This means that if you get an absolute Z-score greater than 2.58, it means you are 99% confident that the data point is significantly different (greater or lesser) than the population mean.
The Z-score greater than 2.58 also refers to p < 0.01 and leads to the rejection of the null hypothesis.