Analysis Toolpak has a number of useful statical tools that we will explore in our that we have explored in analysis tutorials.
Anova: Single Factor 2. Anova: Two-Factor with Replication 3. Anova: Two-Factor without Replication 4. Correlation 5. Covariance 6. Descriptive Statistics 7. Exponential Smoothing 8. F-Test Two Sample for Variance 9. Fourier Analysis Histogram Moving Average Random Number Generation Rank and Percentile Regression What if it affected the results of the students in a negative way?
Or what kind of music would be a good choice for this? Considering all this, it would be immensely helpful to have some proof that it actually works. To figure this out, we decided to implement it on a smaller group of randomly selected students from three different classes. The idea is similar to conducting a survey. We take three different groups of ten randomly selected students all of the same age from three different classrooms.
Each classroom was provided with a different environment for students to study. Classroom A had constant music being played in the background, classroom B had variable music being played and classroom C was a regular class with no music playing. After one month, we conducted a test for all the three groups and collected their test scores. The test scores that we obtained were as follows:. So, in our case,. Looking at the above table, we might assume that the mean score of students from Group A is definitely greater than the other two groups, so the treatment must be helpful.
This leads to a few questions, like:. To answer all these questions, first we will calculate the F-statistic which can be expressed as the ratio of Between Group variability and Within Group Variability. If our test returns a significant f-statistic, we may need to run a post-hoc test to tell us exactly which groups have a difference in means.
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Step 1: Input your data into columns or rows in Excel. For example, if three groups of students for music treatment are being tested, spread the data into three columns. Here, we can see that the F-value is greater than the F-critical value for the alpha level selected 0.
Therefore, we have evidence to reject the null hypothesis and say that at least one of the three samples have significantly different means and thus belong to an entirely different population. If the p-value is less than the alpha level selected which it is, in our case , we reject the Null Hypothesis. There are various methods for finding out which are the samples that represent two different populations. Now to check which samples had different means we will take the Bonferroni approach and perform the post hoc test in Excel.
Step Select an output range. Whereas for B vs C it is much greater than the significance level. This means that B and C belong to the same population. So, it is clear that A constant music group belongs to an entirely different population. Or we can say that the constant music had a significant effect on the performance of students. The music experiment actually helped in improving the results of the students. It works in the same way as R 2 for t-tests. It is used to calculate how much proportion of the variability between the samples is due to the between group difference.
It is calculated as:. Hence Eta square helps us conclude whether the independent variable is really having an impact on the dependent variable or the difference is due to chance or any other factor. Using one-way ANOVA, we found out that the music treatment was helpful in improving the test results of our students. But this treatment was conducted on students of the same age. What if the treatment was to affect different age groups of students in different ways? Or maybe the treatment had varying effects depending upon the teacher who taught the class.
Moreover, how can we be sure as to which factor s is affecting the results of the students more? It means that the variable music treatment did not have any significant effect on the students. Rather a new factor, age, will be introduced to find out how the treatment performs when applied to students of different age groups. This time our dataset looks like this:. Here, there are two factors — class group and age group with two and three levels respectively.
So we now have six different groups of students based on different permutations of class groups and age groups and each different group has a sample size of 5 students. The main effect is similar to a one-way ANOVA where the effect of music and age would be measured separately. Whereas, the interaction effect is the one where both music and age are considered at the same time.
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Two null hypotheses will be tested if we have placed only one observation in each cell. For this example, those hypotheses will be: H1 : All the music treatment groups have equal mean score. H2 : All the age groups have equal mean score. Before we proceed with the calculation, have a look at the image below.
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It will help us better understand the terms used in the formulas. We will see in some time that these two are responsible for the main effect produced. This term will be responsible for the interaction effect produced when both the factors are considered at the same time. And we are already familiar with the , which is the sum of all the observations test scores , irrespective of the factors.
We have calculated all the means — sound class mean, age group mean and mean of every group combination in the above table. Now, calculate the sum of squares SS and degrees of freedom df for sound class, age group and interaction between factor and levels. Since we have more than one source of variation main effects and interaction effects , it is obvious that we will have more than one F-statistic also. Now using these variances, we compute the value of F-statistic for the main and interaction effect.
So, the values of f-statistic are,. If, for a particular effect, its F value is greater than its respective F-critical value calculated using the F-Table , then we reject the null hypothesis for that particular effect.
Make sure you include all of your data, including headers and group names. Rows per sample is actually a bit misleading. What this is asking you is how many individuals are in each group. Step 5: Select an Output Range. Step 6: Select an alpha level. In most cases, an alpha level of 0. The data will be returned in your specified output range. Step 8: Read the results. We can also use the same function for three, four, five or more number of variables.
As you can see in the highlighted cells in the image above, the F-value for sample and column, i. This means that the factors have a significant effect on the results of the students and thus we can reject the null hypothesis for the factors. Also, the F-value for interaction effect is quite less than its F-critical value, so we can conclude that music and age did not have any combined effect on the population.
Until now, we were making conclusions on the performance of students based on just one test. Could there be a possibility that the music treatment helped improve the results of a subject like mathematics but would affect the results adversely for a theoretical subject like history?
ANOVA different sample sizes
So again, we take two groups of randomly selected students from a class and subject each group to one kind of music environment, i. In the above example, this would be to factor in the effect of gender on the medication. For example, gender in the subjects taking the medication is known but is not to be analyzed.
The Anova dialog box opens.
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Drag the cursor across the cells to be analyzed in the workbook. This article was written by the It Still Works team, copy edited and fact checked through a multi-point auditing system, in efforts to ensure our readers only receive the best information. To submit your questions or ideas, or to simply learn more about It Still Works, contact us. Video of the Day.