Sampling is used in hypothesis testing.If the null hypothesis is true, the statistical significance is calculated using a p-value.The null hypothesis can be accepted if the p-value is less than 0.05).A simple t-test can be used to determine the significance of two different groups of a dataset.
Step 1: Do you have 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.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 experimental data.Students who read the material before class get better final grades.
Step 2: Set the significance level so that your data can be considered significant.
The threshold that you set to determine significance is called the significance level.The data is considered statistically 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 chance of observing the differences seen in your data is just 5%.The results are more significant if the confidence level is higher and the p-value is lower.To get higher confidence in your data, set the p-value to 0.01.When detecting flaws in products, lower p-values are used.It is important to have high confidence that the parts will work as they are supposed to.A significance level of 0.05 is acceptable for most hypothesis-driven experiments.
Step 3: Decide to use one or twotailed tests.
A t-test makes assumptions about the distribution of your data.The majority of the samples are 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.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 test for significance in either direction.If you know which direction you want your data to go, you can use a one-tailed test.You will use a one-tailed test if you expect the student's grades to improve.
Step 4: Determine sample size with a power analysis.
The power of a test depends on the sample size.The threshold for power is 80%.You need some information about your expected means between each group and their standard deviations in a power analysis.To find 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: The formula for standard deviation should be defined.
The standard deviation is a measure 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.The standard deviation is s.You will sum all of the values collected.Each individual value is represented by xi.The mean is the average of your data for each group.The total sample number is N.
Step 6: Take the samples from each group.
The standard deviation can be calculated by taking the average of the samples in individual groups.The Greek letter mu is the average.Simply add each sample together and divide by the total number of samples.To find the average grade of the group that read the material before class, we need to look at some data.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 the sample.
The next part of the equation involves the part.Each sample will be subtracted from the average.You will end up with five subtractings.The final score was 98.6, (93- 88.6), (83- 86.9), and (94- 88.6).The numbers are now 1.4, 2.4, 3.6, and 5.4.
Step 8: Add the numbers together with a square.
The new numbers will 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 it.We are working with 1.96, 5.76, 12.96, 31.36, and 29.16 in our example.Summing these squares together yields 81.2.
Step 9: Divide the sample number by its total 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 should be taken.
The square root of the final number is the sample number minus one.The standard deviation is calculated using 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 two sample groups.
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 experimental groups.The formula for variance is sd.The difference between your groups is called sd.The sample size of group 1 is N1, while the standard deviation is s1.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: The t-score of your data can be calculated.
You can use a t-score to convert your data into a form that allows you to compare it to other data.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 of the first group is 1.The second group's average is 2.The difference between your samples is called 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 degrees of freedom for the 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 an example.There are five samples in the first group and five in second group.
Step 14: Evaluate significance using 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 is 8 d.f.The p-value for a one-tailed test is 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 material before class get better final grades.
Step 15: You should consider a follow up study.
A small pilot study helps researchers understand how to design a larger study.If you do another study with more measurements, 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.