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


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?

Results

            A correlational analysis was conducted to examine the relationship between negative mood and self-esteem.  The analysis was significant, r(122) = -.49,

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



Correlation Statement Spacing


                                    * Same spacing applies for F statements.