Unit 4: Correlation PS503 Applied Psych Stats. Unit 5 Project In this project you will be doing a correlation as well as a regression The instruction

Unit 4: Correlation

PS503

Applied Psych Stats

Unit 5 Project In this project you will be doing a

correlation as well as a regression The instruction document is much more

complete than the one for the first project

It gives a little background on the dataset as well as describing the variables we will be looking at

Unit 5 Project I’ve gone through the instructions given

and if you follow them you should get the required outputs.

Make sure you use the rubric, it’s long, but that’s because it breaks down the points in units of 5 or 10.

Unit 5 Project You are doing TWO analyses in this project. 1) A correlation using Pearson’s r to look at

the relationship (if any) between a person’s assertiveness as measured on the Rathus Assertiveness Scale and whether or not they “express anger openly” as measured in a subscale, “axout” of the Crowne-Marlowe scale

Unit 5 Project You are doing TWO analyses in this project. 2) A regression asking “Is there a relationship

between one’s tendency to hold one’s anger in (‘axin”) and one’s score on the Crowne-Marlowe Social Desirability scale

Unit 5 Project The first analysis

We are looking at whether or not there is a correlation between assertiveness, as measured by the Rathus Assertiveness Scale (variable named “rath”) and a person’s tendency to openly express anger (the “axout” variable)

One’s assertiveness might cause one to be openly expressive, but we can’t be sure that there is a causal relationship here.

Thus, a correlation is the best option


The output will consist of two tables “Descriptive statistics”

With the mean, standard deviation, and N for each variable “Correlations”

With the correlations for the variables This output may be confusing because SPSS correlates

each variable against each variable including themselves. I have an image on the next slide

Unit 5 Project The upper left

corner correlates rath to itself, so it’s meaningless

The lower right corner correlates axout to itself, so it’s meaningless, too

Ignore these

Unit 5 Project Both the upper right and

lower left are identical: they are both the correlations of rath:axout

You will want to report the r value displayed here and the p value (“Sig.”)

The red blocks will not be in your output


So what will the results mean? We will assume that a higher value on rath means

greater assertiveness We will assume that a higher value on axout

means greater tendency to express anger openly Armed with this knowledge you should be able to

draw the correct conclusion from the following:

Unit 5 Project The first analysis - possible conclusions:

If r is not significant: we cannot predict one from the other: they appear to not have a relationship

If r is significant and positive: we can assume that a higher score on one scale predicts a higher score on the other: that someone who is more assertive is likely to be more expressive of their anger

If r is significant and negative: we can assume that a higher score on one scale predicts a lower score on the other: that someone who is more assertive is likely to be less expressive of their anger


You should do a summary of this first analysis before moving on to the second

This is the sort of thing you will see in papers, it helps the reader keep things together.

An example follows:

Unit 5 Project The first analysis - examples of what to write if significant or not

An analysis of the correlation between assertiveness (as measured on the Rathus Assertiveness Scale) and the tendency to outwardly express anger (as measured by the Crowne-Marlowe Social Desirability Scale) was performed on the data. The Pearson’s correlation was significant, r = [value], p < 0.05, indicating that there is a [weak/moderate/strong] correlation between the two variables: individuals with a greater assertiveness will generally have a [greater/lesser] tendency to express anger.

Items in brackets differ depending upon r value An analysis of the correlation between assertiveness (as measured on the

Rathus Assertiveness Scale) and the tendency to outwardly express anger (as measured by the Crowne-Marlowe Social Desirability Scale) was performed on the data. The Pearson’s correlation was not significant, r = [value], p > 0.05, indicating that there is not a correlation between the two variables: it is impossible to predict one characteristic from the other.

Unit 5 Project The second analysis

We are looking at whether or not there is a relationship between the Crowne-Marlowe variable and the tendency to hold anger in.

The Crowne-Marlowe variable is a measure of how likely a person is to behave in ways that are more socially desirable. A higher score indicates that the person is more likely to behave in ways that they believe are socially desirable.

We are using a regression because it will provide us with both

an r-value, showing us how predictive, how correlated, one is with the other

A within-subjects ANOVA


Your output will consist of six tables Descriptive statistics Correlations Variables Entered/Removed (ignore this one) Model Summary ANOVA Coefficients


The Correlations table is the one where you can find the R value of interest.

The value also shows up in the “Model Summary” table but the negative sign (if there is one) is dropped from this table and so your conclusions might be wrong if you used this to figure out R.

The rubric first asks you to talk about the R value and what it means, which is very much like the first section of this paper

The rubric then wants you to discuss the ANOVA results. Remember to report the F-test results with the degrees of freedom.


You are also asked to discuss the table listed “Coefficients.” You need to report the standardized coefficient for axin and

describe what that and the unstandardized coefficients mean.

You can find discussion of the unstandardized coefficients on page 338 of the text: they are the intercept and slope of the data if plotted on an x,y axis

Standardized coefficients are used when one has standardized the data to fit the z-distribution (page 356-7)

Finally, you need to be able to talk about the confidence intervals for axin, which are really just another way of talking about the standard error of the means


Finally, summarize for the reader what this all means, both analyses.

Assume the writer is NOT a statistician or stats specialist… Pretend you are trying to explain the results to your parent or

sibling.

Unit 5 Project

Structure: Clear, complete paragraphs, clear and logical organizationthroughout, moves fluidly between sections. Primarily student’s own wordswith quotes used very sparingly, includes several references to supportconclusions.

Mechanics: Uses correct grammar, spelling, punctuation, and APA style.Free of typographical errors, double-spaced, 6-8 pages in length (notincluding the cover page or reference page).


If you have questions, email me… Start on this sooner rather than later… If you run into a snag and you just started on Monday or

Tuesday of unit 5, I may not get back to you until it’s late and you wind up getting a late penalty.

Unit 4 - Correlation We’ve been discussing this on the DB. Have you specific questions about it?

Unit 4 - Chi Square This is a little different from the other

stuff we’ve been doing With Chi-square we can look at

quantities and see if they are occurring in the patterns expected

Unit 4 - Chi Square What we do with the Chi-square is compare

the frequency data that we see with the frequency data that we would expect

If the variation between what we observe and what is expected is too great, we reach “significance” and must conclude that the data are NOT fitting into the expected distribution

Unit 4 - Chi Square Chi-square is useful when you have variables

and counts of members of the various variables.

What other sorts of things could this be used for?

Unit 4 - Chi Square Chi-square is useful when you have variables

and counts of members of the various variables.

What other sorts of things could this be used for? Determining if an organization is being

discriminatory in its hiring or promotion practices Determining if graduation rates between schools

are comparable Many more…

Unit 4 - Chi Square For example:

A professor claims that his grading follows the following pattern:

As & Fs = 10% of the grades, each Bs & Ds = 15% of the grades, each Cs comprise the remaining 50% of the

grades


Due to a complaint regarding unfair grading, an administration person looks at the distribution of grades in the professor’s previous two classes

As = 27; Bs = 42, Cs = 123, Ds =45 ; Fs = 13 For the two classes, combined, N = 250 (the

total number of students)


Observed results: A = 27; B = 42; C = 123; D = 45 ; F = 13 For the two classes, combined, N = 250

Expected results (for a class of 250): A = 25; B = 37.5; C = 125; D = 37.5; F = 25 Expected values may be fractional

Are these significantly different? There seem to be a lot of Fs…


O :: A = 27; B = 42; C = 123; D = 45 ; F = 13 E :: A = 25; B = 37.5; C = 125; D = 37.5; F = 25 We use Chi-square (goodness-of-fit) to

determine if the observed values match the expected values (H0) or do not (H1)

X2 = ∑ (O-E)2/E It looks complex, it’s really very simple ∑ means to take the sum of the things to the

right of it


O :: A = 27; B = 42; C = 123; D = 45 ; F = 13 E :: A = 25; B = 37.5; C = 125; D = 37.5; F = 25 X2 = ∑ (O-E)2/E The observed value minus the expected value Square the result Divide that result by the expected value Repeat for all matching Os & Es and sum the

result


O :: A = 27; B = 42; C = 123; D = 45 ; F = 13 E :: A = 25; B = 37.5; C = 125; D = 37.5; F = 25 X2 = ∑ (O-E)2/E In this case it becomes the following: X2 = (27-25)2/25 + (42-37.5)2/37.5 +

(123-125)2/125 + (45-37.5)2/37.5 + (13-25)2/25 X2 = 22/25 + 4.52/37.5 + -22/125 + 7.52/37.5 + -122/25 X2 = 0.16 + 0.54 + 0.032 + 1.5 + 5.76 = 7.992


O :: A = 27; B = 42; C = 123; D = 45 ; F = 13 E :: A = 25; B = 37.5; C = 125; D = 37.5; F = 25 X2 = ∑ (O-E)2/E Thus, Chi-square is solved: X2 = 7.992, with four degrees of freedom

One variable: grade, five levels, minus one On page 988 of the text is a table of critical values for

Chi-square At the 0.05 level for df= 4, the Critical value is 9.49


O :: A = 27; B = 42; C = 123; D = 45 ; F = 13 E :: A = 25; B = 37.5; C = 125; D = 37.5; F = 25 X2 = ∑ (O-E)2/E Thus, Chi-square is solved: X2 = 7.992, with four degrees of freedom At the 0.05 level for df= 4, the Critical value is 9.49 Since the calculated value is less than the critical value,

we have no significance: the professor is grading within his policy

Unit 4 - Chi Square By the way, that table on page 988 has a number of

other tables before and after it. The one just before it is the table of critical values of the F-test. Before that is the t-test. There are several others here.

Before computers could calculate the exact “p” value for you (“Sig” in SPSS) these critical values were used to determine if we had reached significance… if the F-test (or t-test or Chi-square) gave a value above the correct critical value, you had reached significance.

These tables are somewhat archaic now that computers can compute the exact p-value for you.

Unit 4 - Chi Square Questions? Chi-square is nice because it’s fairly easy to calculate

by hand.

Documents

Unit 4: Correlation PS503 Applied Psych Stats. Unit 5 Project In this project you will be doing a correlation as well as a regression The instruction