## Research Paper Writing Results For Anova

## Three or four things to report

You will be reporting three or four things, depending on whether you find a significant result for your 1-Way Betwee Subjects ANOVA

## 1. Test type and use

You want to tell your reader what type of analysis you conducted. This will help your reader make sense of your results. You also want to tell your reader why this particular analysis was used. What did your analysis test for?

## Example

You can report data from your own experiments by using the template below.

“A one-way between subjects ANOVA was conducted to compare the effect of (IV)______________ on (DV)_______________ in _________________,

__________________, and __________________ conditions.”

If we were reporting data for our example, we might write a sentence like this.

“A one-way between subjects ANOVA was conducted to compare the effect of sugar on memory for words in sugar, a little sugar and no sugar conditions.”

## 2. Significant differences between conditions

You want to tell your reader whether or not there was a significant difference between condition means. You can report data from your own experiments by using the template below.

“There was a significant (not a significant) effect of IV ____________ on DV ______________ at the p<.05 level for the three conditions [F(___, ___) = ___, p = ____].

## Just fill in the blanks by using the SPSS output

Let’s fill in the values. You are reporting the degrees of freedom (df), the F value (F) and the Sig. value (often referred to as the p value).

## Once the blanks are full…

You have a sentence that looks very scientific but was actually very simple to produce.

“There was a significant effect of amount of sugar on words remembered at the p<.05 level for the three conditions [F(2, 12) = 4.94, p = 0.027].”

## 3. Only if result of test was significant, report results of post hoc tests

In the previous chapter on interpretation, you learned that the significance value generated in a 1-Way Between Subjects ANOVA doesn’t tell you everything. If you find a significant effect using this type of test, you can conclude that there is a significant difference between some of the conditions in your experiment. However, you will not know where this effect exists. The significant difference could be between any or all of the conditions in your experiment. In the previous chapter, you learned that to determine where significance exists you need to conduct a post hoc test to compare each condition with all other conditions. If you have an IV with 3 levels, like the one in this example, you would need to conduct and report the results of a post hoc test to report which conditions are significantly different from which other conditions.

## Example

Because we have found a statistically significant result in this example, we needed to compute a post hoc test. We selected the Tukey post hoc test. This test is designed to compare each of our conditions to every other conditions. This test will compare the Sugar and No Sugar conditions. It will also compare the A little sugar and No Sugar conditions. It will also compare the A Little Sugar and Sugar conditions. The results of the Tukey post hoc must be reported if you find a significant effect for your overall ANOVA.

You can use the following template to report the results of your Tukey post hoc test. Just fill in the means and standard deviation values for each condition. They are located in your Descriptives box.

If you used this template with our example, you would end up with a sentence that looks something like this.

“Post hoc comparisons using the Tukey HSD test indicated that the mean score for the sugar condition (M = 4.20, SD = 1.30) was significantly different than the no sugar condition (M = 2.20, SD = 0.84). However, the a little sugar condition (M = 3.60, SD = 0.89) did not significantly differ from the sugar and no sugar conditions.”

## 4. Report your results in words that people can understand

Since it might be hard for someone to figure out what that sentence means or how it relates to your experiment, you want to briefly recap in words that people can understand. Try to imagine trying to explain your results to someone who is not familiar with science. In one sentence, explain your results in easy to understand language.

## Example

You might write something like this for our example.

“Taken together, these results suggest that high levels of sugar really do have an effect on memory for words. Specifically, our results suggest that when humans consume high levels of sugar, they remember more words. However, it should be noted that sugar level must be high in order to see an effect. Medium sugar levels do not appear to significantly increase word memory.”

This sentence is so much easier to understand than the scientific one with all of the numbers in it.

## Let’s see how this looks all together

When you put the three main components together, results look something like this.

“A one-way between subjects ANOVA was conducted to compare the effect of sugar on memory for words in sugar, a little sugar and no sugar conditions. There was a significant effect of amount of sugar on words remembered at the p<.05 level for the three conditions [F(2, 12) = 4.94, p = 0.027]. Post hoc comparisons using the Tukey HSD test indicated that the mean score for the sugar condition (M = 4.20, SD = 1.30) was significantly different than the no sugar condition (M = 2.20, SD = 0.84). However, the a little sugar condition (M = 3.60, SD = 0.89) did not significantly differ from the sugar and no sugar conditions. Taken together, these results suggest that high levels of sugar really do have an effect on memory for words. Specifically, our results suggest that when humans consume high levels of sugar, they remember more words. However, it should be noted that sugar level must be high in order to see an effect. Medium sugar levels do not appear to significantly increase word memory.”

Looks pretty complicated but it is simple when you know how to write each part.

** Background | Enter Data | Analyze Data | Interpret Data | Report Data **

**Where Do I Find the Values for the F-Statement?**

back to Experimental Homepage

Recall that when you are writing up a results section you want to cover three things:

a) Tell the reader the analysis that was conducted.

b) Whether the analysis was significant including the appropriate statistical "proof."

c) Describe what the analysis means in words. Be sure to include means and standard deviations either in the text or in a table.

Below you will find descriptive information and an analysis of variance summary table. This table is from an experiment that investigated whether physically attractive vs. unattractive defendants in a criminal case would be rated differently on amount of guilt (GUILTY) and length of prison sentence (PRISON). Because there is only one independent variable (attractiveness of the defendant), this analysis is referred to as a one-way analysis of variance. If there were two independent variables, then the analysis would be referred to as two-way analysis of variance.

**Oneway**

A good results section for the analysis on guilt ratings would be:

Results

The effect size r was calculated for all appropriate analyses (Rosenthal, 1991).

Guilt Ratings (Margin headings are useful to tell the reader what the paragraph will be about. Format it correctly).

A one-way analysis of variance (ANOVA) was calculated on participants' ratings of defendant guilt. The analysis was not significant, *F*(1, 37) = 1.20,

*p* = .281 (*r *= .18).

If the "Guilty" analysis had been significant, then it would be correct to describe the mean differences in the following manner:

Participants who read about an unattractive defendant rated the defendant more guilty (*M* = 6.50, *SD* = 1.85) than participants who read about an

attractive defendant (*M* = 5.79, *SD* = 2.20).

Try writing the results for the analysis on length of prison sentence ratings...I'll get you started.

Length of Prison Sentence Ratings (Margin headings are useful to tell the reader what the paragraph will be about. Format it correctly).

A one-way ANOVA was calculated on participants' ratings of length of prison sentence for the defendant. The analysis was significant, *F*( , ) = ,

*p *= .xxx (*r* = ).

Once you understand the results from a one-way ANOVA, try to figure out a more sophisticated ANOVA by clicking here.

**What goes in the " F ( , )"?**

The information contained in the "*F*( , )" can be most easily found in the analysis of variance summary table under the "df" column. This information is the degrees of freedom (df) for your experiment. Specifically, the degrees of freedom in the numerator (between groups) and the degrees of freedom in the denominator (within groups or error). The first number is your between groups degrees of freedom followed by your within groups degrees of freedom. Because your degrees of freedom are dependent on the number of participants you have in each of your conditions, your degrees of freedom may change from analysis to analysis.

**What comes after the "="?**

The information that comes after the "=" is the actual value of that *F*. This value can be found in the analysis of variance summary table under the "F" column.

**How Do I Know if the Analysis is Significant?**

Simple. All you need to do to determine whether that particular analysis is significant is to, again, look at the analysis of variance summary table under the "Sig." column. The "Sig." column is your probability level for that particular analysis. Remember, any value in this column that is LESS than .05 is significant. All other values in that column that are greater than .05 are NOT significant. But, I KNOW you remember all of this from your statistics class...right?

**What is " r"?**

"*r*" is an effect size. There is a very simple formula for calculating *r*. You can find the formula for r and more information on effect sizes by following this link or the "(*r* = .18)" link above under the "Guilt Ratings" heading.

**One-Way Analysis of Variance with Three Groups**

Below you will find descriptive information and an analysis of variance summary table. This table is from an experiment that investigated whether the type of music that song lyrics were attributed to would differently impact whether participants thought the lyrics were objectionable (OBJECT) and whether they thought the lyrics should have a mandatory warning label (WARN). This analysis differs from the one above, because the independent variable (type of music) has three levels. When you have an independent variable that has three or more levels, then you must run comparisons among the levels (e.g., country vs. rap, country vs. heavy metal, rap vs. heavy metal) for each of the dependent variables.

The write-up for the lyric objection results could be as follows:

**Results**

The effect size *r* was calculated for all appropriate analyses (Rosenthal, 1991).

Objection to the Lyrics

A one-way analysis of variance (ANOVA) was calculated on participants' ratings of objection to the lyrics. The analysis was significant, *F*(2, 61) = 5.33,

*p* = .007. Participants found the lyrics more objectionable when they were attributed to rap music (*M* = 6.25, *SD* = 2.71) than when the lyrics were attributed to

heavy metal (*M* = 5.10, *SD* = 0.63) or country music (*M* = 3.91, *SD* = 2.92). Comparisons indicated that the rap music condition was significantly different from

the country music condition, *t*(61) = -3.26, *p* = .002, *r* = .39. The rap music condition was not significantly different from the heavy metal condition, *t*(61) =

1.58, *p* = .120, *r* = .20. The country music condition was not significantly different from the heavy metal music condition, *t*(61) = -1.67, *p* = .100, *r* = .21.

**Note:* Unless the effect size you are using is obscure, there is no reason to state it. The sentence below "**Results**" is there to show you how you would reference it

should you report an effect size that is not commonly used.

To make sure you understand, you should write up the results for whether the lyrics should have a mandatory warning label (WARN).

Correlational Analyses

Suppose we wanted to examine the relationship between self-esteem and negative mood. First, we should remember that scores on the Rosenberg self-esteem scale range from 10 to 50 with higher scores indicating higher self-esteem. The measure of negative mood ranges from 12 to 60 with higher scores indicating more negative mood. We get 122 undergraduates to complete both measures, enter the data, run the analysis, and get the following:

How do we write this up in a results section?

*r*(120) = -.49,

*p*< .001. Participants with higher self-esteem scores reported less negative mood.

Correlation Statement Spacing

* Same spacing applies for F statements.

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