Statistical analysis is used to guide hypothesis testing.If the null hypothesis is true, the statistical significance is calculated using a p-value, which tells you the probability of your result being observed.The null hypothesis can be assumed to be false if the p-value is less than the significance level set.The significance between two different groups of a dataset can be determined using a simple t-test.
Step 1: Do you have any hypotheses?
The first step in assessing statistical significance is defining the question you want to answer.The hypothesis is a statement about the differences in the population.There is a null and an alternative hypothesis for any experiment.You will compare two groups to see if they are the same or different.There is no difference between your two data sets according to the null hypothesis.Students who read before class don't get better final grades.The alternative hypothesis is the opposite of the null hypothesis and you are trying to support it with your data.Students who read the material before class get better grades.
Step 2: To determine how unusual your data is, set the significance level.
The threshold that you set to determine significance is called the significance level.The data is considered significant if it is less than or equal to the set significance level.The significance level is usually set to 0.05, meaning that the probability of observing the differences seen in your data is just 5%.The results are more significant if the confidence level is higher.If you want to have more confidence in your data, set the p-value to 0.01.In manufacturing, lower p-values are used to detect flaws.It is important to have high confidence that every part will work as it is supposed to.The significance level is acceptable for most hypothesis-driven experiments.
Step 3: Decide if you want to use a one- or two-tailed test.
A t-test makes assumptions about the distribution of your data.The majority of the samples fall in the middle of a bell curve.The t-test is a mathematical test to see if your data falls outside of the normal distribution, either above or below the curve.A one-tailed test examines the potential of a relationship in a single direction, while a two-tailing test looks at the relationship's potential in both directions.If you don't know if your data will be above or below the control group, use a two-tailed test.You can use this to test for significance in either direction.Use a one-tailed test if you know which direction you want your data to go.You will use a one-tailed test when you expect the student's grades to improve.
Step 4: Determine sample size using a power analysis.
The power of a test is based on the sample size.The threshold for power is 80%.A power analysis can be difficult without some preliminary data, as you need to know your expected means between each group and their standard deviations.To determine the optimal sample size for your data, use a power analysis calculator.The sample size needed for a larger, comprehensive study is usually determined by a small pilot study.If you don't have the means to do a complex pilot study, you can use the literature and studies that other people have done.This is a good place to start.
Step 5: Define the formula for deviation.
The standard deviation is a measurement of how much data you have.It helps you determine if the data is significant by giving you information on how similar each data point is.The equation may seem complicated at first, but these steps will show you how to calculate it.The formula is s.Standard deviation is what it is.You will sum all of the values collected.Each value is represented by xi.The mean and average of your data for each group.The total sample number is N.
Step 6: The samples in each group should be averaged.
The standard deviation can be calculated by taking the average of the samples in individual groups.The Greek letter mu is what the average is.Simply add each sample together and then divide by the total number of samples.Let's look at some data to find the average grade of the group that read the material before class.We will use a dataset of 5 points: 90, 91, 85, 83, and 94.Add all the samples together.The sum is divided by the sample number.This group has an average grade of 88.6.
Step 7: The average should be subtracted from each sample.
The next part of the equation involves the part.You will subtract the average from each sample.You will end up with five subtractings.The final score was 98.6, (93- 88.6), (84- 86.9), and (94- 88.6).The numbers are now 1.4, 2.4, -3.6, and 5.4.
Step 8: Add all of the numbers together.
The new numbers will now be squared.Any negative signs will be taken care of by this step.If you have a negative sign after this step or at the end of your calculation, you may have forgotten.We are now working with 1.96, 5.76, 12.96, 31.36, and 29.16 in our example.Summing these squares together yields a total of 81.2.
Step 9: Divide by the total sample number.
You are taking a sample of the population of all students to make an estimation because you haven't counted an entire population.Divide: 81.2/4 by 20.3
Step 10: The root is called the square root.
Take the square root of the final number if you divide it by one.The standard deviation is calculated by this last step.There are statistical programs that can do this calculation for you.Our example shows the standard deviation of the final grades of students who read before class.
Step 11: The difference between the 2 sample groups should be calculated.
The example only deals with 1 of the sample groups.You will have data from both if you compare 2 groups.The standard deviation of the second group of samples is used to calculate the variance between the 2 groups.The formula for variance is sd.The difference between your groups is referred to as sd.The standard deviation of group 1 and N1 is the sample size.The data from group 2 had a sample size of 5 and a standard deviation of 5.81.The difference is: sd is ((s1)/N1).
Step 12: Determine the t-score of your data.
You can convert your data into a form that allows you to compare it to other data with a t-score.T-scores allow you to calculate the probability of two groups being different from each other.There is a formula for a t- score.The average is the first group.The second group's average is 2.The difference between your samples is known as sd.You will not have a negative t-value if you use the larger average.The sample average for group 2 was 80.The t-score is: 2.61.
Step 13: Determine the degree of freedom for your sample.
The number of degrees of freedom is determined using the sample size.Take the number of samples from each group and subtract two.The degrees of freedom is our example.There are five samples in the first group and five in second group.
Step 14: To evaluate significance, use a t table.
A table of t-scores and degrees of freedom can be found in a statistics book.You can find the p-value that matches your t-score by looking at the row containing the degrees of freedom.There was 8 d.f.The p-value for a one-tailed test falls between 0.01 and 0.025.Our data is statistically significant because our significance level is less than or equal to 0.05.We reject the null hypothesis and accept the alternative hypothesis that students who read the material before class get better final grades.
Step 15: Consider a follow up study.
A small pilot study is used to help researchers understand how to design a larger study.If you do another study with more data, you will be more confident in your conclusion.Failure to observe a difference when there is one, or false acceptance of the null are types of errors that can be determined by a follow-up study.