H0: # of retweets per tweet ( bees = zika = mosquito ) H1: # of retweets per tweet ( bees > zika | mosquito )To start off, we need to isolate the tweets that have embedded images. I have determined that the easiest and most accurate way to identify an embedded image is to look for “photo/1” in the parsed_media_url field of the data set:
zqimage <- zq[grep("photo/1", zq$parsed_media_url),]This leaves us with 83,266 tweets that have images embedded in them. Now, the hashtags are stuck within the “hashes” column, and are delimited by semicolons. Using tidyr, we can separate those out into more columns:
library("tidyr") zq1 <- separate(zqimage, col = hashes, into = c("hash1", "hash2", "hash3", "hash4", "hash5", "hash6", "hash7", "hash8", "hash9", "hash10", "hash11", "hash12", "hash13", "hash14", "hash15", "hash16", "hash17", "hash18", "hash19", "hash20"), sep = ";", extra = "merge", fill = "right")This adds 19 more columns, which should then either have their own hashtag, or a N/A value. From here, we can use apply to count up the frequency of each hashtag and create a table to show us what the 30 most popular hashtags are:
library("plyr") hashes <- apply(zq1[,24:43], 2, FUN=function(x) plyr::count(x)) hashes <- do.call(rbind.data.frame, hashes) hashes <- plyr::ddply(hashes,"x",numcolwise(sum)) hashes <- hashes[!is.na(hashes[,1]),] hashes <- head(arrange(hashes,desc(freq)), n = 100)The hashtags I want to compare are “bees” and “mosquito” which are the 14th and 30th most common hashtags, respectively. In order to do further analysis, I need to subset the rows to only include the max value of retweet_count for each unique tweet. I’m going to do it to zqimage instead of the hashes object so that I can use grep on the non separated hashes column later:
library("dplyr") zqimage <- zq[grep("photo/1", zq$parsed_media_url),] zqimage <- zqimage %>% group_by(text) %>% filter(retweet_count == max(retweet_count), favorite_count == max(favorite_count)) zqimage <- arrange(zqimage, desc(retweet_count))I want to compare the contributions between hash tags, so I can get rid of any rows that don’t have any hashtags
zqimage <- zqimage[!is.na(zqimage$hashes), ]This leaves us with 9,651 unique tweets that have hashtags and have embedded images. In order to conduct an ANOVA test we need to categorize the tweets. In order to do so, we need to create a new column that says if the tweets have “bees”, “mosquito”, or “zika” in them
zqimage$hashhash <- ifelse(grepl("bees", zqimage$hashes, ignore.case = TRUE), "bees", ifelse(grepl("mosquito", zqimage$hashes, ignore.case = TRUE), "mosquito", ifelse(grepl("zika", zqimage$hashes, ignore.case = TRUE), "zika", "Other")))From here, we can apply the ANOVA test
fit <- aov(zqimage$retweet_count ~ hashhash, data = zqimage)Making a boxplot of the data shows something very telling It looks like there’s an oppressive amount of tweets with abnormally high values of retweets that are making it hard to see what’s going on, so lets look at a log scale of only the tweets that have been retweeted.
zqn0 <- zqimage[!zqimage$retweet_count == 0,] boxplot(log(zqn0$retweet_count) ~ zqn0$hashhashFrom there, we can see clearly that hashtags with bees performs better than mosquito, but it looks almost neck-and-neck with zika. If we look at the values of fit$coefficients, we can see that bees edges out zika in performance too.
> fit$coefficients (Intercept) hashhashmosquito hashhashOther hashhashzika 7.1780822 -4.9327290 -4.8003600 -0.9336632I used the granovagg package to create the above graphic which again shows that bees outperforms mosquito, even though mosquito had nearly an order of magnitude fewer hashtags than case-insensitive “bees”, and it also outperforms case-insensitive “zika” despite the fact that zika hashtags had over 22,000 more hashtags. The p value for the hashes is very small, causing us to fail to reject the null hypothesis and accept the alternate hypothesis that the bees hashtags perform better than the mosquito or zika hash tags.
Null hypothesis: The proportion of people who choose the same hotel again will be the same for beach combers and windsurfers.
To start off, I constructed my data.frame in a very roundabout manner:
>Beachcomber <- c(163,64,227) >Windsurfer <- c(154,108,262) >Choose_again <- c("Yes", "No", "Total") >dat <- data.frame(Choose_again, Beachcomber, Windsurfer) >dat$Total <- dat$Beachcomber + dat$Windsurfer >dat <- dat[,-1] >rownames(dat) <- c("Yes", "no","total") >dat Beachcomber Windsurfer Total Yes 163 154 317 no 64 108 172 total 227 262 489
Next, I run the chi-test and save it in an object:
>res<-chisq.test(dat[1:2,1:2]) > res Pearson's Chi-squared test with Yates' continuity correction data: dat[1:2, 1:2] X-squared = 8.4903, df = 1, p-value = 0.0035
I was stuck on that for a while, trying to figure out exactly which parts of the data.frame needed to be included/excluded. I did notice that this way of doing it didn’t give me the error that other combinations did though. I assume it’s because the function implemented Yates’ continuity correction, which is automatically implemented for 2×2 tables. The p-value is quite small, so at a threshold of p=.05, the null hypothesis would be rejected and we’d say that it appears that the proportion of people who choose to return to their hotel is different for each group.
gg <- data.frame(x = seq(0,20,.1)) gg$y <- dchisq(gg$x, 1) ggplot(gg) + geom_path(aes(x,y)) + geom_ribbon(data=gg[gg$x>qchisq(.05,1,lower.tail=FALSE),], aes(x,ymin=0, ymax=y), fill="red")+ geom_vline(xintercept = res$statistic, color = "blue")+ labs( x = "x", y = "dchisq(gg$x, 1)")+ geom_text(aes(x=8, label="x^2", y=0.25), colour="blue", angle=90)
> high <- c(10,9,8,9,10,8)) > moderate <- c(8,10,6,7,8,8) > low <- c(4,6,6,4,2,2) > reaction <- c(10,9,8,9,10,8,8,10,6,7,8,8,4,6,6,4,2,2) > stresslvls <- c(rep("high",6), rep("moderate",6), rep("low",6)) > dat <- data.frame(reaction,stresslvls) > analysis <- lm(reaction ~ as.factor(stresslvls), data = dat) > anova(analysis) Analysis of Variance Table Response: stress Df Sum Sq Mean Sq F value Pr(>F) as.factor(stresslvls) 2 82.111 41.056 21.358 4.082e-05 *** Residuals 15 28.833 1.922 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The ANOVA test essentially breaks a sample down into smaller groups and compares the variance between the means of each of those groups to determine how much variance can be attributed to chance.
Here, we have analyzed a grouping of the reaction times of participants that were subjected to various levels of stress. Above, we can see the return of the ANOVA test. We can see that the between-group mean sum of squares is 41.056. This shows that the difference between each of the individual sample means and the mean of all the samples. The F value is the ratio between the mean squares of the mean squares. The larger the F statistic is, the more you can rule out the difference between the means being due to chance. The fact that the P value is so small allows us to reject the null hypothesis and claim that the level of stress the participants are subjected does have an effect on their reaction times.
- The mean for males is 3.571429 and the mean for females is 7.6
- The degrees of freedom for the t.test is 6.7687
- The T statistic is 2.8651
- The P value is 0.02505
- +- 2.576
1a. H0: A cookie will break at more than 70 pounds of force or greater; u >= 70
Ha: A cookie will break at less than 70 pounds of force on average; u < 70
1c. p = 0.0359 There’s a 3.59% chance of finding a sample mean of 69.1 if u >=70.
1d. p = 0.0002 since p < 0.5, there is enough evidence to dismiss H0
1e. p = 0.0227 since p < 0.5, there is enough evidence to dismiss H0
2a. cor(mod8$Cost.per.serving, mod8$Fibber.per.serving)
Q1. I created a function to do the calculations to find mu for the Confidence Interval:
ci <- function(xbar, con, sig, n)
con1 = con + ((1-con)/2)
mu = xbar + (qnorm(con1) * (sig / sqrt(n)))
sn = xbar – (qnorm(con1) * (sig / sqrt(n)))
paste(“The confidence interval is between “, sn, ” and “, +mu, ” and the estimated mean is “, xbar, sep =””)
The confidence intervals came in as follows:
> ci(115, .9, 15, 100)
 “The confidence interval is between 112.532719559573 and 117.467280440427 and the estimated mean is 115”
> ci(115, .95, 15, 100)
 “The confidence interval is between 112.06005402319 and 117.93994597681 and the estimated mean is 115”
> ci(115, .98, 15, 100)
 “The confidence interval is between 111.510478188939 and 118.489521811061 and the estimated mean is 115”
 “The confidence interval is between 83.0400360154599 and 86.9599639845401 and the estimated mean is 85”
((1.96 * 15) / 5)^2
I think the minimum sample size should be 35 if I’m thinking of the zscore tails properly.
edit: After reviewing the last question, 35 is right, but how i got to it was wrong
The biggest thing to note about this is the difference between the 95% confidence interval and the 97.5th percentile ranking. Each tail of the 95% confidence interval contains 2.5% of the area under the curve. But we’re only looking for a single tailed value, so we must use qnorm(.975).
I feel like I was perhaps a little bit confused about what questions 1 and 2 were asking for, or what the answer should look like.
Import vector of values of ice cream purchase numbers
>a <- c(8, 14, 16, 10, 11)
Generate random sample of 2 values and save to a vector
> b <- sample(a,2)
 10 11
Calculate mean and standard deviation of the sample.
Create data.frame out of mean and stdev for the sample and population.
smp <- c(10.5,0.7071068)
> pop <- c(11.8,3.193744)
> c <- data.frame < (smp, pop)
- I think that the sample proportion will have the approximately the same distribution since nq = 5.
- I think 100 is the smallest value of n for which p is approximately normal because anything smaller than n = 100 will make np < 5. The high value of p is very limiting.
Initially, I was just going to calculate the correlation coefficient manually in R without using the functions, but then I decided that if I was going to do it manually then I may as well do it by hand. I ended up making a mistake with spacing by not thinking about how many digits would be made out of squaring an already triple digit number.
From there, inputting the x and y values into R and executing the cor.tests() were very simple and straightforward. I feel like I’ve gotten to the point with R where I don’t feel like I’m completely lost all the time.
For this assignment, I decided to to make everything as one script and use the Source with Echo command to run it all at once. The only issue I had is that mode() does not yield a mode. It returns what storage mode the object uses, so I had to look up how to make a function to calculate the mode.
From there, I was able to call mat and matrange to pull up the tables of all the values.