A researcher investigated the effect of volume of background noise on participants’accuracy rates while performing a difficult task. He tested three groups of randomly selected students and obtained the following means and sums of squares:

Volume
Source Sum of sqs. df Mean sq
Between 652.16 ______ ______ ______
F_______
Within 612.75 ______ ______
total 1264.92 ______
(a) Complete the ANOVA. (b) At á = .05, what is Fcrit? (c) Report the statistical results in the proper format. (d) Perform the appropriate post hoc tests. (e) What do you conclude about this study? (f) Compute the effect size and interpret it.
Please help.... Thank you in advance

Looks like you might be filling in a table for a one-way ANOVA test.

Your ANOVA summary table has the following setup:

Source.....SS.....df.....MS.....F
Between
Within
Totals

Here are a few hints:

SS total = SS between + SS within

To calculate df between:
k - 1
Note: k = number of levels or groups.

To calculate df within:
N - k
Note: N = total number of values in all levels or groups.

df total = df between + df within

To calculate MS between:
SS between/df between

To calculate MS within:
SS within/df within

To calculate F-ratio:
MS between/MS within

After filling in the table and finding the F-ratio, find the critical or cutoff value to reject the null using an F-table at .05 level of significance. Compare to the F-ratio to determine whether or not to reject the null. If the null is rejected, there is a difference. If the null is not rejected, there is no difference.

Use the Tukey procedure to compare all possible pairs of means to determine which differs.

I hope this brief summary will help get you started.

To complete the ANOVA, we need to fill in the missing values in the table. The information provided is:

Between-groups sum of squares (SSB) = 652.16
Between-groups degrees of freedom (dfb) = ?
Between-groups mean squares (MSB) = ?

Within-groups sum of squares (SSW) = 612.75
Within-groups degrees of freedom (dfw) = ?
Within-groups mean squares (MSW) = ?

Total sum of squares (SST) = 1264.92
Total degrees of freedom (dft) = ?
Total mean squares (MST) = ?

To calculate the missing values, we can use the following formulas:

dfb = number of groups - 1
dfw = total number of participants - number of groups
dft = dfb + dfw

MSB = SSB / dfb
MSW = SSW / dfw
MST = SST / dft

In this case, the number of groups is not provided, so we'll have to assume it or use additional information. Once we have the number of groups, we can calculate the missing values.

(b) To find the critical F-value (Fcrit) at α = .05, we need the degrees of freedom for the numerator (dfb) and denominator (dfw). Once we have these values, we can use a statistical table or an online calculator to determine Fcrit.

(c) To report the statistical results in the proper format, you should include the F-value, degrees of freedom, and p-value. For example: "The analysis of variance revealed a significant effect of volume of background noise on accuracy rates, F(df numerator, df denominator) = F-value, p < .05."

(d) Post hoc tests are performed when there is a significant difference between groups. Typically, Tukey's HSD or Bonferroni tests are used for pairwise comparisons to determine which specific groups differ significantly from each other.

(e) To conclude about this study, you would need to examine the statistical results. If there is a significant effect of volume of background noise, you can say that it has an impact on participants' accuracy rates. However, without additional information, it is difficult to draw any further conclusions.

(f) To compute the effect size, you can use different measures such as Eta-squared (η²) or Omega-squared (ω²). Eta-squared represents the proportion of variance explained by the independent variable, while Omega-squared is a less biased estimation of the effect size. These calculations require the sum of squares from the ANOVA.

Given the missing values, it's not possible to calculate the effect size without additional information or assumptions.