You find the significance of results. You analyze the data and run experiments. However, business relevance is different from statistical significance. Many business organizations could not distinguish between the two and misuse and misunderstand the concept. On the other hand, analyzing the data properly helps in making suitable business decisions. That is the reason why managers should understand the concept of statistical significance.
What is Statistical Significance?
Statistical significance indicates that a variable’s relationship towards another variable is not a coincidence but because of another factor on that variable. In easy words, statistical significance is a mathematical representation of the reliability of the statistics. In this article, you will learn how to calculate statistical significance between two factors.
Calculating Statistical Significance
You can understand the concept and find an extensive answer by calculating the statistical significance by hand. You can use a calculator. Here are the steps that you can follow to calculate the statistical significance:
1.Creating a Null Hypothesis
First of all, you need to determine the null hypothesis. You can find out if there is a difference in the data set you are using. You should never believe your null hypothesis, as this is only a guess.
2.Creating an Alternative Hypothesis
Now, find out the alternative hypothesis. When you find the alternative hypothesis, you will know if there is a relationship between your data. The alternative hypothesis is opposite to the null hypothesis that you find previously.
3.Determining Significance Level
After finding the null and alternate hypothesis, you will determine the significance level or alpha. There is a possibility that you have to reject your null hypothesis even though it might be true. The standard alpha is 0.05 to 5 percent.
4.Choosing the Type of Test
Now decide what test you will choose from, one-tailed or two-tailed. However, the one-tailed test distribution area is one-sided, and for the two-tailed test, it is two-sided. In simple words, in one-tailed tests, you will analyze the two variables’ relationship in a single direction and two directions in two-sided tests. If your samples are one-sided, then your alternative hypothesis is true.
5.Performing Power Analysis for Sample Size
Power analysis will help you determine the sample size. To find the power analysis, you should know the statistical power, significance level, sample size, and effect size. You need to use a calculator to perform these calculations. By staying in a degree of confidence, this method will help you determine the sample size. This method will help you find a suitable sample size so you can calculate statistical significance. For instance, if the sample size is very small, you will not find an accurate outcome.
6.Calculating Standard Deviation
Now, calculate the standard deviation. To do that, you need to use the following formula:
Standard deviation = √ ((∑|x−μ|^ 2) / (N-1))
In this equation:
- ∑ =is the data sum
- x =is the individual data
- μ = is the mean of the data for each group
- N =is the total sample
With this calculation, you can find out how to spread the mean value and expected value. Find the variance between the groups if you have more sample groups.
7.Using Standard Error Formula
After that, use the standard error formula. Here is the formula to find the standard error of the two groups by the standard deviation.
Standard error =√((s1/N1) + (s2/N2))
In this equation:
s1 =is the standard deviation (first group)
N1 =is the sample size (first group)
s2 =is the standard deviation (second group)
N2 =is the sample size (second group)
In this step, you need to find the t-score. Use the below equation to find the t-score:
t =((µ1–µ2) / (sd))
In this equation
t =is the t-score
µ1 =average (first group)
µ2 =average (second group)
sd =is the standard error
9.Finding Degrees of Freedom
Now, find out the degrees of freedom. Here is the formula to find the degrees of freedom:
degrees of freedom =(s1 + s2) – 2
In this equation
s1 =samples (first group)
s2 =samples (second group)
Now, you can calculate your statistical significance with the help of the t-table. First, look for the degrees of freedom on the left side and determine the variance. Now, go upwards and find the p-value of each variable. Then, compare the significance level or alpha with the p-value. You can consider a p-value below 0.05 as statistically significant.
What is P-Value?
The probability of finding the results is called P-value. For instance, you are comparing the weights of US citizens in New York and California. You should start with the null hypothesis that New Yorkers have more average weight than Californians.
Now suppose you perform the study to find if the null hypothesis is true or not. After the study, you find that New Yorkers’ average weight is 20 lbs more than California, with 0.41 as a P-value. This means that the null hypothesis is true, and New Yorkers weigh more than Californians. Now there is a 47% chance that you will measure 20 lbs more weight of New Yorkers.
But if New Yorkers don’t weigh more, you still have to measure it 20 lbs higher due to noise in your data almost half of the time. So lower P-value means more accurate results as it means that there is less noise in the data.
You can use statistical significance to find the validity of the tests and analysis. However, this does not mean that you have accurate data. Many surveys can provide incorrect information through unsuitable data. Furthermore, you may be using demographics with bias in representation.
Moreover, your insights will be inaccurate if you run your statistical significance test poorly. People mostly face this issue when their significance level (α) is wrong. There is a possibility that your P-value is a false positive. However, to counter this problem, you can repeat the study. If you find low P-value than the previous, you have reduced the false positivity from your outcome.