# Competition

1. Create a null hypothesis - The first step in calculating statistical significance is to determine your null hypothesis. Your null hypothesis should state that there is no significant difference between the sets of data you're using. Keep in mind that you don't need to believe the null hypothesis.

2. Create an alternative hypothesis - Next, create an alternative hypothesis. Typically, your alternative hypothesis is the opposite of your null hypothesis since it'll state that there is, in fact, a statistically significant relationship between your data sets.

3. Determine the significance level - Your next step involves determining the significance level or rather, the alpha. This refers to the likelihood of rejecting the null hypothesis even when it's true. A common alpha is 0.05 or five percent.

4. Decide on the type of test you'll use - Next, you'll need to determine if you'll use a one-tailed test or a two-tailed test. Whereas the critical area of distribution is one-sided in a one-tailed test, it's two-sided in a two-tailed test. In other words, one-tailed tests analyze the relationship between two variables in one direction and two-tailed tests analyze the relationship between two variables in two directions. If the sample you're using lands within the one-sided critical area, the alternative hypothesis is considered true.

5. Perform a power analysis to find out your sample size - You'll then need to do a power analysis to determine your sample size. A power analysis involves the effect size, sample size, significance level and statistical power. For this step, consider using a calculator. This type of analysis allows you to see the sample size you'll need to determine the effect of a given test within a degree of confidence. In other words, it'll let you know what sample size is suitable to determine statistical significance. For example, if your sample size ends up being too small, it won't give you an accurate result.

6. Calculate the standard deviation - Next, you'll need to calculate the standard deviation. To this, you'll use the following formula:

standard deviation = √((∑|x−μ|^ 2) / (N-1))

where:

∑ = the sum of the data

x = individual data

μ = the data's mean for each group

N = the total sample

Performing this calculation will let you know how to spread out your measurements are about the mean or expected value. If you have more than one sample group, you'll also need to determine the variance between the sample groups.

7. Use the standard error formula - Next, you'll need to use the standard error formula. For our purposes, let's say you have two standard deviations for your two groups. The standard error formula is as follows:

standard error = √((s1/N1) + (s2/N2))

where:

s1 = the standard deviation of your first group

N1 = group one's sample size

s2 = the standard deviation of your second group

N2 = group two's sample size

8. Determine t-score - For the next step, you'll need to find the t-score. The equation for this is as follows:

t = ((µ1–µ2) / (sd))

where:

t = the t-score

µ1 = group one's average

µ2 = group two's average

sd = standard error

9. Find the degrees of freedom - Next, you'll need to determine the degrees of freedom. The formula for this is as follows:

degrees of freedom = (s1 + s2) - 2

where:

s1 = samples of group 1

s2 = samples of group 2

10. Use a t-table - Finally, you'll calculate the statistical significance using a t-table. Start by looking at the left side of your degrees of freedom and find your variance. Then, go upward to see the p-values. Compare the p-value to the significance level or rather, the alpha. Remember that a p-value less than 0.05 is considered statistically significant.