We are going to use the same data that we useD to conduct the ANOVA by hand to conduct an ANOVA in SPSS.
Because this is a small data set we're going to create the whole data set from scratch,
And then we will conduct a one-way ANOVA in SPSS.
Here is the research story for our one-way ANOVA .
Following a series of complaints about wicked witches, the wizard of Oz conducts a study to determine if certain regions of oz
Have more problems with wicked witches than other regions.
he randomly surveys 5 munchkins from each of four regions and
Records the number of complaints that he received about wicked witchiness from each one. Is
there a difference in which wickedness between regions?
Let's start by entering the data in SPSS.
Open up SPSSon your desktop and open a new blank dataset.
In variable view we will create two variableS. The first is region,
which is nominal.
The second variable is complaints, and that
will be scaled.
For both variables set the decimals to 0.
Now we will set the levels of the region factor.
For region
label 1 = North region,
2 = South region,
3 = East region, and 4 = West region.
For Label "Region where witches live"
For the scale variable Complaints, label it "Complaints about wicked witches"
Now go to Data View so that we can enter some data.
Let's start with the complaints. Enter the data for each region in order.
Now we should add the numbers corresponding to each region. The first five were from the north region. Which we have labeled as 1.
The second five are from the South region, which we label this 2.
The third five are from the East
region which is 3, and the last five are from the west region which is 4.
Now that the data have been entered, save your data set as WickedWitch.sav
Save it to the desktop and we are ready to run a one-way ANOVA.
You will conduct a one-way ANOVA by going to Analyze
Compare Means
One-Way ANOVA
We are seeing the variable labels now.
Right-click on any variable and select "Display Variable Name" if you want to see the names instead of the labels.
The dependent variable will require us moving the scale variable Complaints into the dependent list box
Factor is the categorical variable region. No need to define groups like we did with an independent samples t-test
The ANOVA will run whatever number of groups we have defined in our factor, which in our case is 4.
Now click on Post Hoc. We have a lot of options.
Because each region has the same number of participants, or munchkins, we will select Tukey for our post hoc.
However, we will need to check assumptions for our ANOVA, and if we end up with unequal variances we will need to use the Games-Howell
post hoc. So let's save some time and get the Games-Howell post hoc now as well. Click Continue.
Now click on Options...
Select Descriptive to get the means and standard deviations,
homogeneity of variance test for Levene's test,
Welch(in case we find that the assumptions were violated), and
the means plot so that we can see a line graph of the means.
Click Continue, and then OK.
When the output window opens we can begin to interpret the results.
This first box contains the descriptive statistics.
These are broken down by each region and the total.
Here we can see sample size,
mean,
standard deviation and,
the standard error of the mean for each group. We also have confidence intervals and
the minimum and maximum scores.
You keep looking at this output,
I am going to return to the slides so that I can point out some specific things about the interpretation.
Before interpreting the ANOVA we should first check the assumptions of the test, one of which is
homogeneity of variances, which is tested by Levene's test.
Check out my video on Levene's test for more explanation about using Levene's test to test for
homogeneity of variances.
As with any
between-subjects model, the Lavenw statistic is testing the assumption of homogeneity of variance.
We see here that Levene's statistic is not even close to
significant, .918, which is great
because the Levine statistic is not significant the groups are not statistically significantly different.
This is what we want. This matches our assumption that the groups have equal or homogeneous variance.
Good, that means that we will not need the Welch ANOVA test or the Games-Howell post hoc either.
Well this takes us to the F table.
The first thing you should notice is that the columns are out of order to the F table that I showed you earlier.
The F table that I showed you is in APA style.
This table is not.
This reinforces the idea that you should never use raw SPSS output in place of APA formatted tables
the output will always require additional formatting.
I will also point out that this is a simplified table that is generated when you use the compare means command, the one that we used.
There is a more complex table that will be generated if you do your ANOVA using the general linear model command.
To interpret and report this ANOVA, we would report the name of the test (F)
followed by degrees of freedom between and within (3 and 16) and the F value (10.49).
Next is the p-value
You would never report significance as .000 because the probability is not actually 0.
Instead you would report p < .05
And the last eta squared value is an effect size that I will show you in the next video about effect sizes in ANOVA.
As you scroll down you will also encounter the Welch's robust test for equality of means or Welch's ANOVA.
If we had examined Levene's test and found that it was
significant so that the assumption of homogeneity of variance had been violated,
then we would interpret using Welch's ANOVA and
If significant, the Games-Howell post hoc.
I have another video illustrating this situation for now. You can ignore this output because we do not need it.
So one treatment is different than the other treatments, but we need the post hoc to find out which one.
This is a table of post hoc results. Each region is compared to the other three regions.
You see the mean difference,
the standard error of the mean difference, and the significance value for each comparison.
As before, if a region differs by less than .05 in the Sig. column those differences are
statistically significant.
We can see that the north region is not different than the south region, p = .937
But north is different than both east and west.
Regions with probabilities of .008 and .001.
We could continue doing these comparisons or we could evaluate the homogeneous subsets.
The SPSS output will create subsets for groups that are the same as each other.
Subsets that differ will be in different columns.
Here the north and the south region are both in the same subset. We also see that their means 1 and
1.4 are displayed.
The east and west regions are also in the same subset,
so they are the same as each other, but they are different than the first subset for the North and South region.
North and South are in the same group. We'll call that Low Complaints and
East and West are in the same group which we could call High Complaints.
The North and South group is significantly different than the East and West group,
but the regions within the groups are not significantly different from each other, and
This is how you could write up the results in APA style.
Feel free to pause and read it if you're working on a write-up. You'll see that
I listed the means and standard deviations for each group that comes from the descriptive statistics at the very top of your output window
The last statement about the meaning of the findings would actually go in your discussion section if you were writing this up for a paper.