Our fictitious dataset contains a number of different variables. Our independent variable, therefore, is Education, which has three levels — High School, Graduate and PostGrad — and our dependent variable is Frisbee Throwing Distance i. The one-way ANOVA test allows us to determine whether there is a significant difference in the mean distances thrown by each of the groups. You can do this by dragging and dropping, or by highlighting a variable, and then clicking on the appropriate arrow in the middle of the dialog.

The ANOVA test will tell you whether there is a significant difference between the means of two or more levels of a variable. You need to do a post hoc test to find this out. You should select Tukey, as shown above, and ensure that your significance level is set to 0. At the very least, you should select the Homogeneity of variance test option since homogeneity of variance is required for the ANOVA test.

Descriptive statistics and a Means plot are also useful. Review your options, and click the OK button. In particular, the data analysis shows that the subjects in the PostGrad group throw the frisbee quite a bit further than subjects in the other two groups.

The key question, of course, is whether the difference in mean scores reaches significance. We have tested this using the Levene statistic. In our example, as you can see above, the significance value of the Levene statistic based on a comparison of medians is. In our example, we have a significant result. The value of F is 3. This means there is a statistically significant difference between the means of the different levels of the education variable.

For this we need to look at the result of the post hoc Tukey HSD test. You should now be able to perform a one-way ANOVA test in SPSS, check the homogeneity of variance assumption has been met, run a post hoc test, and interpret and report your result.The independent, or unpaired, t-test is a statistical measure of the difference between the means of two independent and identically distributed samples.

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For example, you may want to test to determine if there is a difference between the cholesterol levels of men and women. This test computes a t value for the data that is then related to a p-value for the determination of significance.

One of the most recognized statistical programs is SPSS, which generates a variety of test results for sets of data. You can use SPSS to generate two tables for the results of an independent t-test.

Find the Group Statistics Table in the data output. This table reports general descriptive statistical values such as mean, standard deviation, etc. Interpret the N values as the number of samples tested in each of the two groups for the t-test.

For example, comparing the cholesterol levels of men and women would have two N values of andrespectively. Find the standard deviation values and relate them to the data sets. The standard deviation identifies how close the set of data points within each test group are to their respective means.

Thus, a higher standard deviation signifies that the data is more spread out over a wide range of values as compared to a smaller standard of deviation.

Observe the standard error mean value for the two test groups. This value is calculated from the standard deviation and sample size of the population and identifies the precision of the mean of each sample. A smaller standard error indicates that the mean is more likely to be that of the true population.

Find the Independent Samples Test Table in the data output. This table gives the actual results from the t-test. Check to determine if the variance in the two test groups are similar. Choose which column of numbers you need to use based on whether you have equal or unequal variances. Thus, a narrower confidence interval provides more conclusive results and a better estimation of the actual population than a broader confidence interval.

Ensure that your two data sets are both normally distributed or the results may not be valid. Matt Perdue is a medical student at an allopathic U. Beginning inhe began writing science-related articles for eHow. He was also authored a paper for a medical journal exploring current recommendations for bone scans to diagnose osteoporosis. Things You'll Need.

About the Author. Photo Credits. Copyright Leaf Group Ltd.A repeated-measures ANOVA design is sometimes used to analyze data from a longitudinal study, where the requirement is to assess the effect of the passage of time on a particular variable.

The average score for a person with a spider phobia is 23, which compares to a score of slightly under 3 for a non-phobic. SPQ is the dependent variable. The null hypothesis is that the mean SPQ score is the same for all levels of the within-subjects factor. This will bring up the Repeated Measures Define Factor s dialog box.

And we have 3 levels, so input 3 into Number of Levels. Then click Add. Click on the Define button, which will bring up the Repeated Measures dialog blox.

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You can drag and drop, or use the arrow button in the middle of the box. Click on the Options button. The most recent version of SPSS 26 has an options dialog box that looks like this. You want to display descriptive statistics and estimates of effect size, so tick these options in the Display section as above. You should be looking at the original Repeated Measures dialog box.

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The descriptive statistics that SPSS outputs are easy enough to understand. The comparison between means see above gives us an idea of the direction of any possible effect. In our example, it seems as if fear of spiders increases over time, with the greatest increase A requirement that must be met before you can trust the p -value generated by the standard repeated-measures ANOVA is the homogeneity-of-variance-of-differences or sphericity assumption.

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Our p -value is. This assumption is frequently violated. Happily SPSS does this work for you. As we have just discussed, our data meets the assumption of sphericity, which means we can read our result straight from the top row Sphericity Assumed.

The value of F is 5. This means there is a statistically significant difference between the means of the different levels of the within-subjects variable time. If our data had not met the assumption of sphericity, we would need to use one of the alternative univariate tests.

This is where pairwise comparisons come into play.In these results, the null hypothesis states that the mean hardness values of 4 different paints are equal. Because the p-value is 0. Interpret these intervals carefully because making multiple comparisons increases the type 1 error rate. That is, when you increase the number of comparisons, you also increase the probability that at least one comparison will incorrectly conclude that one of the observed differences is significantly different.

To assess the differences that appear on this plot, use the grouping information table and other comparisons output shown in step 3. In the interval plot, Blend 2 has the lowest mean and Blend 4 has the highest. You cannot determine from this graph whether any differences are statistically significant. To determine statistical significance, assess the confidence intervals for the differences of means.

If your one-way ANOVA p-value is less than your significance level, you know that some of the group means are different, but not which pairs of groups. Use the grouping information table and tests for differences of means to determine whether the mean difference between specific pairs of groups are statistically significant and to estimate by how much they are different.

For more information on comparison methods, go to Using multiple comparisons to assess differences in group means. Use the grouping information table to quickly determine whether the mean difference between any pair of groups is statistically significant. Use the confidence intervals to determine likely ranges for the differences and to determine whether the differences are practically significant. The table displays a set of confidence intervals for the difference between pairs of means. The interval plot for differences of means displays the same information. Confidence intervals that do not contain zero indicate a mean difference that is statistically significant. The percentage of times that a single confidence interval includes the true difference between one pair of group means, if you repeat the study multiple times.

The percentage of times that a set of confidence intervals includes the true differences for all group comparisons, if you repeat the study multiple times. Controlling the simultaneous confidence level is particularly important when you perform multiple comparisons.

If you do not control the simultaneous confidence level, the chance that at least one confidence interval does not contain the true difference increases with the number of comparisons. In these results, the table shows that group A contains Blends 1, 3, and 4, and group B contains Blends 1, 2, and 3. Blends 1 and 3 are in both groups. Differences between means that share a letter are not statistically significant.

Blends 2 and 4 do not share a letter, which indicates that Blend 4 has a significantly higher mean than Blend 2.In this section, we show you the main tables required to understand your results from the two-way ANOVA, including descriptives, between-subjects effects, Tukey post hoc tests multiple comparisonsa plot of the results, and how to write up these results.

For a complete explanation of the output you have to interpret when checking your data for the six assumptions required to carry out a two-way ANOVA, see our enhanced guide. This includes relevant boxplots, and output from your Shapiro-Wilk test for normality and test for homogeneity of variances. Finally, if you have a statistically significant interaction, you will also need to report simple main effects. Alternately, if you do not have a statistically significant interaction, there are other procedures you will have to follow.

Below, we take you through each of the main tables required to understand your results from the two-way ANOVA. You can find appropriate descriptive statistics for when you report the results of your two-way ANOVA in the aptly named " Descriptive Statistics " table, as shown below:. This table is very useful because it provides the mean and standard deviation for each combination of the groups of the independent variables what is sometimes referred to as each "cell" of the design.

In addition, the table provides "Total" rows, which allows means and standard deviations for groups only split by one independent variable, or none at all, to be known.

This might be more useful if you do not have a statistically significant interaction. Although this graph is probably not of sufficient quality to present in your reports you can edit its look in SPSS Statisticsit does tend to provide a good graphical illustration of your results. An interaction effect can usually be seen as a set of non-parallel lines. You can see from this graph that the lines do not appear to be parallel with the lines actually crossing.

You might expect there to be a statistically significant interaction, which we can confirm in the next section. The actual result of the two-way ANOVA — namely, whether either of the two independent variables or their interaction are statistically significant — is shown in the Tests of Between-Subjects Effects table, as shown below:.

You can see from the " Sig. When you have a statistically significant interactionreporting the main effects can be misleading.

### Regression Analysis | SPSS Annotated Output

Therefore, you will need to report the simple main effects. In our example, this would involve determining the mean difference in interest in politics between genders at each educational level, as well as between educational level for each gender. Unfortunately, SPSS Statistics does not allow you to do this using the graphical interface you will be familiar with, but requires you to use syntax. Therefore, in our enhanced two-way ANOVA guide, we show you the procedure for doing this in SPSS Statistics, as well as explaining how to interpret and write up the output from your simple main effects.

When you do not have a statistically significant interaction, we explain two options you have, as well as a procedure you can use in SPSS Statistics to deal with this issue. If you do not have a statistically significant interaction, you might interpret the Tukey post hoc test results for the different levels of education, which can be found in the Multiple Comparisons table, as shown below:.

You can see from the table above that there is some repetition of the results, but regardless of which row we choose to read from, we are interested in the differences between 1 School and College, 2 School and University, and 3 College and University.A farmer wants to know which fertilizer is best for his parsley plants.

### Repeated-Measures ANOVA in SPSS, Including Interpretation

So he tries different fertilizers on different plants and weighs these plants after 6 weeks. The data -partly shown below- are in parsley. After opening our data in SPSSlet's first see what they basically look like. A quick way for doing so is inspecting a histogram of weights for each fertilizer separately.

The screenshot below guides you through. After following these steps, clicking P aste results in the syntax below. Let's run it. Importantly, these distributions look plausible and we don't see any outliers: our data seem correct to begin with -not always the case with real-world data! Conclusion: the vast majority of weights are between some 40 and 65 grams and they seem reasonably normally distributed. Precisely how did the fertilizers affect the plants?

Let's compare some descriptive statistics for fertilizers separately.

## SPSS tutorials

Now, this table tells us a lot about our samples of plants. But what do our sample means say about the population means? Can we say anything about the effects of fertilizers on all future plants? We'll try to do so by refuting the statement that all fertilizers perform equally: our null hypothesis. If this is true, then our sample means will probably differ a bit anyway.

However, very different sample means contradict the hypothesis that the population means are equal. In this case, we may conclude that this null hypothesis probably wasn't true after all. ANOVA will basically tells us to what extent our null hypothesis is credible. However, it requires some assumptions regarding our data. So how to check if we meet these assumptions? And what to do if we violate them? The simple flowchart below guides us through. So why do we inspect our sample sizes based on a means table? Why didn't we just look at the frequency distribution for fertilizer? And our means table shows precisely those. A second reason is that we need to report the means and standard deviations per group.The name Analysis Of Variance was derived based on the approach in which the method uses the variance to determine the means whether they are different or equal.

## How to Interpret Results Using ANOVA Test

It is a statistical method used to test the differences between two or more means. It is used to test general differences rather than specific differences among means.

Null hypothesis states that all population means are equal. The alternative hypothesis proves that at least one population mean is different. The reason for performing ANOVA is to see whether any difference exists between the groups on some variable.

Oneway ANOVA SPSS program and interpretation

You can use t-test to compare the means of two samples but when there are more than two samples to be compared then ANOVA is the best method to be used. One Way ANOVA is used to check whether there is any significant difference between the means of three or more unrelated groups. It mainly tests the null hypothesis.

One way ANOVA is an omnibus test statistic and it will not let you know which specific groups were different from each other. In order to know the specific group or groups which differed from others then you need to do a post hoc test.

Their weights are recorded after a few days. The effect of the exercises on the 5 group of men are compared. Here weight is the only one factor. Repeated measures investigate about the 1. You might research the effect of a 6 month exercise programme on weight reducing on some individuals. You calculate the weight at three different point of time during the training period to develop a time-course for any exercise effect. You might indulge the same individual to eat different type of weight reducing food and rate them as per the taste.

In this example the same set of people are measured more than once on the same dependent variable. The main objective of a two way ANOVA is to find out if there is any interaction between the two independent variables on the dependent variables. It also lets you know whether the effect of one of your independent variables on the dependent variable is same for all the values of your other independent variable.

The research of the effect of fertilizers on yield of rice. You apply five fertilizers of different quality on five plots of land each cultivating rice. The yield from each plot of land is recorded and the difference between each plot is observed. Here the effect of the fertility of the plots can also be studied. Thus there are two factors, Fertilizer and Fertility.

The six assumptions are listed below. Two way repeated measures the mean differences between the groups that have been split into two within the independent variables. A two way repeated measure is often used in research where a dependent variable is measured more than twice under two or more conditions. A health researcher wants to find the best way to reduce the chronic joint pain suffered by the people.