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This exercise MUST BE SUBMITTED no later than 1:00 PM on Tuesday, May 3rd. I cannot accept late submissions this time. Grades are due!
First analysis: The dataset is internet.txt.
Some researchers on social media usage and perceived social isolation have proposed that social internet use causes perceived social isolation because it replaces genuine social contact. I want to test an additional idea.
Data from Shelley Stoecker and Christina Rukenbrod Psyc 497 Spring 2006. Scores on a loneliness scale and social anxiety scale and three scores from an internet usage survey.
To get the data:
> file = "http://ww2.coastal.edu/kingw/psyc480/data/internet.txt" > INT = read.table(file=file, header=T)
I propose that social anxiety leads to a lot of internet usage, which replaces genuine social interaction, which then causes loneliness. I have no idea which of those types of internet usage will be important, or which should be entered first, so I'll enter the three kinds of Internet usage as a block in a sequential (hierarchical) regression. (Hint: if you're puzzled by this, then where have you been for the last two weeks. It might help you to go do the third analysis first.)
Here is the beginning of my analysis.
> summary(INT) Lone Soc.Anx GIU LIU SIU Min. : 6.00 Min. : 3.000 Min. : 7.00 Min. : 0.000 Min. :20.00 1st Qu.:11.00 1st Qu.: 6.500 1st Qu.:14.00 1st Qu.: 1.000 1st Qu.:31.50 Median :14.00 Median : 9.000 Median :17.00 Median : 4.000 Median :38.00 Mean :15.09 Mean : 8.405 Mean :17.16 Mean : 5.748 Mean :38.72 3rd Qu.:18.00 3rd Qu.:10.000 3rd Qu.:20.00 3rd Qu.: 9.000 3rd Qu.:45.50 Max. :31.00 Max. :17.000 Max. :27.00 Max. :26.000 Max. :66.00 > dim(INT) [1] 111 5 > cor(INT) Lone Soc.Anx GIU LIU SIU Lone 1.0000000 0.295580990 0.31150040 0.22702970 0.200060929 Soc.Anx 0.2955810 1.000000000 0.11699527 0.11573076 -0.004006136 GIU 0.3115004 0.116995272 1.00000000 0.07370225 -0.015521531 LIU 0.2270297 0.115730762 0.07370225 1.00000000 0.558813056 SIU 0.2000609 -0.004006136 -0.01552153 0.55881306 1.000000000 > source("http://ww2.coastal.edu/kingw/psyc480/functions/rcrit.R") > r.crit(df=109) df alpha 1-tail 2-tail 109.0000 0.0500 0.1569 0.1865
Now do the sequential regression. Create three models: Lone against the intercept, Lone against Soc.Anx, and Lone against Soc.Anx and the three types of internet usage.
Questions 1-12. Use the information produced by this analysis to fill in the following table. Give at least 3 accurate NONZERO decimal places in your answers. (The safest way would be to enter numbers exactly as R prints them out.)
13) Are any of the three correlations between Soc.Anx and internet usage significantly different from zero? A) yes B) no
14) Is this analysis (including the part of it you did) consistent with the theory that the effect of social anxiety on loneliness is, at least in part, mediated through internet usage? If not, why not? A) yes B) no, there was no significant total effect of Soc.Anx on Lone C) no, there was no significant effect of Soc.Anx on any of the potential mediating variables D) no, there was no significant effect of internet usage on Lone
15) The correlation between GIU and LIU was 0.07370225. What kind of a correlation is this? A) Pearson r B) point-biserial C) phi coefficient D) none of the above
16) Without doing any further analysis, if we were to do the regression Lone~GIU+LIU+SIU, can we say which of the types of internet usage would be the most important predictor of Lone? A) GIU B) SIU C) LIU D) no, we can't say
17) Why does df1 have the value that it has in the second step of the sequential regression we did? A) the second step always has this as df1 B) because we entered three predictors at this step C) because the variable entered at this step was categorical with 4 levels D) because it just does, that's why!
18) What is another name for R Square Change? A) R Square Difference B) R Square Increment C) Delta R Squared D) Omega R Squared
19) In the first step of the sequential regression, was R Square Change significantly different from zero? A) yes B) no
20) In the second step of the sequential regression, was R Square Change significantly different from zero? A) yes B) no
21) What percentage of the total variability in Lone scores was accounted for by the two predictors in this model? A) 12.55% B) 21.29% C) less than 1% D) This is not given.
22) Of that amount (question 21), how much was accounted for by the GIU+LIU+SIU step alone? A) none B) 21.29% C) 12.55% D) can't say from the information given
It's also possible to enter the three internet usage variables at the same time like this:
> summary(lm(Lone~Soc.Anx+I(GIU+LIU+SIU),data=INT))
This adds together the three values of internet usage and then enters that sum as a single variable.
23) Would you expect this method to produce the same result as you got above? If not, why not? (Hint: you can always do it for yourself and find out!) A) yes B) no, this is a simultaneous (standard multiple) regression, not a sequential regression C) no, because, besides, nowhere in the above analysis did we have a variable that was created by summing the internet usage variables, so this wouldn't work even if we did it as a sequential regression D) both B and C are correct
24) If we did the sequential regression in four steps (step 1: Soc.Anx, step 2: GIU, step 3: LIU, step 4: SIU), would we end up with the same R Squared value for the model as we did above entering the internet usage variables in a single block? (Hint: same hint, although this really ought to be obvious!) A) yes B) no
Second analysis: The dataset is loneliness.txt.
This is an analysis of Parris Claytor's loneliness data, which we've used in a previous exercise.
# These data are from a Psyc 497 project (Parris Claytor, Fall 2011). # The subjects were given three tests, one of embarrassability ("embarrass"), # one of sense of emotional isolation ("emotiso"), and one of sense of social # isolation ("socialiso"). One case was deleted (by me) because of missing # values on all variables. > file = "http://ww2.coastal.edu/kingw/psyc480/data/loneliness.txt" > loneliness = read.table(file=file, header=T) > summary(loneliness) embarrass emotiso socialiso Min. : 32.00 Min. : 0.00 Min. : 0 1st Qu.: 52.75 1st Qu.: 5.75 1st Qu.: 2 Median : 65.00 Median :11.00 Median : 6 Mean : 64.90 Mean :12.07 Mean : 7 3rd Qu.: 76.25 3rd Qu.:16.00 3rd Qu.:10 Max. :111.00 Max. :40.00 Max. :31 > dim(loneliness) [1] 112 3 > cor(loneliness) embarrass emotiso socialiso embarrass 1.0000000 0.2875657 0.4173950 emotiso 0.2875657 1.0000000 0.6397209 socialiso 0.4173950 0.6397209 1.0000000 > r.crit(110) df alpha 1-tail 2-tail 110.0000 0.0500 0.1562 0.1857
The causal theory is that the effect of embarrassability on emotional isolation is mediated through social isolation.
Now do the mediation analysis using either the lm() function in R or the custom mediate() function that you can retrieve from the website as follows.
> source("http://ww2.coastal.edu/kingw/psyc480/functions/mediate.R")
Questions 25-33. Use this information to fill in the empty boxes in the following table. Once again, at least three NONZERO decimal places please.
34) Was the total effect of embarrassability of emotional isolation statistically significant? If so, give the p-value. A) no B) yes, p = 0.002 C) yes, p = 0.76 D) yes, p < .001
35) Was the direct effect of embarrassability of emotional isolation statistically significant? If so, give the p-value. A) no B) yes, p = 0.002 C) yes, p = 0.76 D) yes, p < .001
36) Was the indirect effect of embarrassability of emotional isolation statistically significant? If so, give the p-value. A) no B) yes, p = 0.002 C) yes, p = 0.76 D) yes, p < .001
37) This is an example of: A) no mediation B) partial mediation C) complete mediation D) none of the above is correct
38) Simple mediation analysis generally requires large samples of 100 or more and significant correlations among all three variables. Did we meet those requirements in this case? A) no B) yes
39) Could this analysis also be done by hierarchical regression? A) yes, and we'd get everything we got from the analysis above B) yes, but we would not get everything we got from the analysis above C) yes, but it might give us a totally different result D) no
40) Was the percent mediation greater than 90%? A) no B) yes
Third analysis: The dataset is aggression.txt
Leigh Ann Waslien's Data, Psyc 497, Fall 1999. The variables are:
We've talked about these data before. My "theory" was that hostility is a trait. There are hostile people and there are nonhostile people. On the other hand, anger is a state. People become angry for a while, then it passes. Anger results in aggression. Thus, the effect of hostility on aggression is mediated through anger. Our mediation result was consistent with that theory.
Not everyone would agree with this theory. There is an old theory of emotion, sometimes attributed to William James, that says we act first and then we feel the emotion. We yell and throw punches, and only then do we realize we are angry. This temporal sequence happens so quickly that we usually don't notice. What we notice is we are angry and we are yelling, and "common sense" tells us we must be yelling because we are angry. Let's test the theory that the behavior comes first followed by the emotion with sequential regression.
hostility -> aggression (of all types) ->anger
I'm going to do the entire analysis for you. All you have to do is fill in the boxes and answer the questions.
> file = "http://ww2.coastal.edu/kingw/psyc480/data/aggression.txt" > AGGR = read.table(file=file, header=T) > summary(AGGR) physag verbag anger hostil Min. :10.00 Min. : 5.00 Min. : 7.00 Min. : 8.0 1st Qu.:14.00 1st Qu.:11.00 1st Qu.:10.50 1st Qu.:11.0 Median :18.00 Median :14.00 Median :13.00 Median :16.0 Mean :19.89 Mean :15.14 Mean :14.83 Mean :16.4 3rd Qu.:22.50 3rd Qu.:17.50 3rd Qu.:16.50 3rd Qu.:20.5 Max. :45.00 Max. :28.00 Max. :33.00 Max. :32.0 > dim(AGGR) [1] 35 4 > cor(AGGR) physag verbag anger hostil physag 1.0000000 0.3937911 0.7510095 0.3211264 verbag 0.3937911 1.0000000 0.5004802 0.3901603 anger 0.7510095 0.5004802 1.0000000 0.4544861 hostil 0.3211264 0.3901603 0.4544861 1.0000000 > r.crit(df=33, alpha=0.05) df alpha 1-tail 2-tail 33.0000 0.0500 0.2826 0.3338 > lm.0=lm(anger~1,data=AGGR) > lm.1=lm(anger~hostil,data=AGGR) > lm.2=lm(anger~hostil+physag+verbag,data=AGGR) > anova(lm.0) Analysis of Variance Table Response: anger Df Sum Sq Mean Sq F value Pr(>F) Residuals 34 1257 36.97 > anova(lm.0,lm.1) Analysis of Variance Table Model 1: anger ~ 1 Model 2: anger ~ hostil Res.Df RSS Df Sum of Sq F Pr(>F) 1 34 1256.97 2 33 997.33 1 259.64 8.5909 0.006092 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 > anova(lm.1,lm.2) Analysis of Variance Table Model 1: anger ~ hostil Model 2: anger ~ hostil + physag + verbag Res.Df RSS Df Sum of Sq F Pr(>F) 1 33 997.33 2 31 451.21 2 546.13 18.761 4.58e-06 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Questions 41-48. Use this information to fill in the empty boxes in the following table. Once again, at least three NONZERO decimal places please.
49) What the heck? First, we find in the exercises that the data are consistent with hostility being mediated through anger to aggression. Now it appears the data are also consistent with the mediation of hostility through aggression to anger. I'm just saying, what the heck? A) this is why the causal theory has to come from another source other than the data; the data can only be consistent with a well formulated causal theory; there is no rule that says the same data can't be consistent with two different theories; we need a better study to differentiate between these two causal theories B) maybe both theories are correct C) obviously, we did something wrong here D) statistics is obviously bogus if we can prove anything from the same data
50) What was the movie I referred to in the lunacy exercise? A) Paper Moon B) Man On The Moon C) Hercules Against the Moon Men D) Moonstruck
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