EDST0213, especially Ella & Maeve – also Mark and Zamzama
Task 1
Load these packages:
library(tidyverse) # load the tidyverse
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.4 ✔ readr 2.1.5
✔ forcats 1.0.0 ✔ stringr 1.5.1
✔ ggplot2 3.5.1 ✔ tibble 3.2.1
✔ lubridate 1.9.3 ✔ tidyr 1.3.1
✔ purrr 1.0.2
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(readxl) #load the readxl package to read excellibrary(kableExtra) # load the kableExtra package
Attaching package: 'kableExtra'
The following object is masked from 'package:dplyr':
group_rows
Import data:
math8 <-read_excel("Grade8NAEP.xls", range ="A9:E19")print(math8, n =10) # display the data
# A tibble: 10 × 5
Year Jurisdiction `All students` `Average scale score` `Standard deviation`
<dbl> <chr> <chr> <dbl> <dbl>
1 2022 National All students 274. 38.9
2 2019 National All students 282. 39.7
3 2017 National All students 283. 38.8
4 2015 National All students 282. 36.9
5 2013 National All students 285. 36.5
6 2011 National All students 284. 36.2
7 2009 National All students 283. 36.4
8 2007 National All students 281. 36.1
9 2005 National All students 279. 36.3
10 2003 National All students 278. 36.2
Task 2
Produce a table for the data from task 1 so that the data is shared in chronological order.
math8 |>arrange(math8, Year) |># arrange by year kable(digits =0) |># set to zero decimal placeskable_styling()
Year
Jurisdiction
All students
Average scale score
Standard deviation
2003
National
All students
278
36
2005
National
All students
279
36
2007
National
All students
281
36
2009
National
All students
283
36
2011
National
All students
284
36
2013
National
All students
285
37
2015
National
All students
282
37
2017
National
All students
283
39
2019
National
All students
282
40
2022
National
All students
274
39
Task 3
Produce a plot of average achievement in 8th grade mathematics on the main NAEP test similar to what was produced on the NAEP website.
ggplot(data = math8) +geom_line(mapping =aes(x = Year, y =`Average scale score`)) +# line graphlabs(title ="Trend in Grade 8 Mathematics Average Scale Scores",subtitle ="Main NAEP: 2003 - 2022" )
Task 4
Produce a similar plot adding horizontal lines indicating the cut scores for Basic, Proficient, and Advanced on this plot.
# Task 4# Produce a similar plot adding horizontal lines indicating the cut scores for Basic, Proficient, and Advanced on this plot.# https://nces.ed.gov/nationsreportcard/mathematics/achieve.aspx#grade8 ggplot(data = math8,mapping =aes(x = Year, y =`Average scale score`)) +geom_line() +labs(title ="Trend in Grade 8 Mathematics Average Score",subtitle ="Main NAEP: 2003 - 2022" ) +ylim(260, 335) +geom_line(mapping =aes(x=Year, y =262, color ="Basic"), linetype=2) +geom_line(mapping =aes(x=Year, y =299, color ="Proficient"), linetype=2) +geom_line(mapping =aes(x=Year, y =333, color ="Advanced"), linetype=2) +theme_gray() +theme(legend.position ="right") +scale_color_manual(breaks=c("Advanced", "Proficient", "Basic"), labels=c("Advanced", "Proficient", "Basic"), values=c("#0047AB", "#228B22", "#FDDA0D"))
Another approach – Zamzama & Mark
Label the horizontal lines with the cut scores for Basic, Proficient, and Advanced.
#Add a text label above basic, proficient, and advanced linesggplot(data = math8) +geom_line(mapping =aes(x = Year, y =`Average scale score`)) +labs(title ="Trend in Grade 8 Mathematics Average Scores",subtitle ="Main NAEP: 2003 - 2022" ) +geom_hline(yintercept =262, linetype ="dashed", color ="red") +geom_hline(yintercept =299, linetype ="dashed", color ="blue") +geom_hline(yintercept =333, linetype ="dashed", color ="green") +#Using 'annotate' add text labels above the linesannotate("text", x=2022, y =262, label ="Basic", vjust =-1 , hjust =+1) +annotate("text", x =2022, y =299, label ="Proficient", vjust =-1 , hjust =+1) +annotate("text", x =2022, y =333, label ="Advanced", vjust =-.3 , hjust =+1)
A solid answer by Ella & Maeve: The addition of lines indicating advanced, proficient, and basic performance on the Grade 8 mathematics test allows someone with limited knowledge of scoring for this test to understand whether or not the average score can be considered good. With the original graph (lines not included) it is difficult to understand what a score of 285 implies, you can only deduce that over time the average scores have decreased. With the lines, however, you can see that a score of 285 is still well below proficient, making it more impactful that overtime these scores have regressed.
Task 5
Add a column that shows the difference in scale scores between the Year in question and 2003.
# Task 5math8 <- math8 |>mutate(diff_scale_score =`Average scale score`-`Average scale score`[Year ==2003]) # add a column that shows the difference in scale scores between the year in question and 2003math8 |>select(Year, diff_scale_score)
For this task, we mutated the data set to include a new column that shows the difference in scale scores between the year in question and 2003. This allows us to see how the average scale scores have changed over time. The code was to subtract the average scale score in 2003 from the average scale score in the year in question.
Task 6
Add another column that shows the difference in Math measured in standard deviations since 2003.
For this task, we mutated the data set to include another new column that shows the difference in math measured in standard deviations since 2003. This allows us to see how the average scale scores have changed over time in terms of standard deviations. The code was to subtract the average scale score in 2003 from the average scale score in the year in question and then divide by the standard deviation.
Task 7
Produce the plot that looks like Figure 5.5 from Measuring Up.
ggplot(data = math8) +geom_line(mapping =aes(x = Year, y = diff_SD)) +# line graphlabs(title ="Trend in Grade 8 Mathematics Average Scale Scores",subtitle ="Main NAEP: 2003 - 2022",y ="Difference in Standard Deviations from 2003", )
Task 8
It appears from the graph that average grade 8 math scores have decreased significantly from 2003 to 2022. Overall, there has been a decrease of 0.1 standard deviations in average math scores for grade 8 - in other words, in 2022, the average math score was 0.1 standard deviations below the average in 2003. While this may seem like a marginal difference, the overall decrease in average test scores implies that there is an issue within math education. It had appeared that from 2003 to around 2012, average scores were displaying an upward trend, with 2012 scores being a whole 0.2 standard deviations above the average in 2003. This upward progression is ideal, however, we see a sharp downward turn by 2015, and a continuous steep downward trend from 2019 to 2023. This particular drop in scores suggests that perhaps these math issues began around 2019. Given the timeframe it is possible that this drop in scores is attributable to the affects of Covid, however, it is important to work towards solutions so that we may see a reappearance of upwards trends in these test scores.
Task 9
mean_2022 <- math8$`Average scale score`[1] #mean in 2022stddev_2022 <- math8$`Standard deviation`[1] #standard deviation in 2022cut_scores <-c(262, 299, 333) #cut scores for basic,prof,adv labels <-c("Basic", "Proficient", "Advanced")cut_data <-data.frame(Score = cut_scores, Label = labels) #data frame for the cut scoresx_values <-seq(mean_2022 -3* stddev_2022, mean_2022 +3* stddev_2022, length.out =100) #x values to make a perfect bell curvey_values <-dnorm(x_values, mean = mean_2022, sd = stddev_2022) #y values for the bell curvedata <-data.frame(Score = x_values, Density = y_values) #data frame for the bell curve# Create the plotggplot(data, aes(x = Score, y = Density)) +# Bell curvegeom_line(color ="blue", size =1) +geom_vline(data = cut_data, aes(xintercept = Score, color = Label), linetype ="dashed", size =0.8) +# Add vertical lines with labelslabs(title ="Normal Distribution of 8th Grade Math Scores (2022)",x ="Score",y ="Density" ) +scale_color_manual(values =c("red", "darkgreen", "purple")) +# Specify colors for the legendtheme(legend.title =element_blank()) # Remove legend title
Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
Reliability Quizzes
Hoffman’s work in front of the class on Tuesday
# Libarieslibrary(tidyverse)# DataPop1 <-c(6, 9, 8, 6, 8, 8, 9, 7, 7, 5, 9)Pop2 <-c(10, 6, 6, 6, 8, 7, 10, 9, 8, 7, 6)# Make a table for these two quizzesdf <-data.frame(Pop1, Pop2)df
# make a scatterplot of df# improve this scatterplot by adding jitterggplot(df, aes(x =jitter(Pop1), y =jitter(Pop2))) +geom_point() +geom_smooth(method ="lm", se =FALSE) +labs(title ="Scatterplot of Pop quiz #1 and Pop quiz #2",x ="Pop1",y ="Pop2") +theme_minimal() +theme(aspect.ratio =1) +scale_x_continuous(limits =c(4, 10)) +scale_y_continuous(limits =c(4, 10))
`geom_smooth()` using formula = 'y ~ x'
Warning: Removed 1 row containing non-finite outside the scale range
(`stat_smooth()`).
Warning: Removed 2 rows containing missing values or values outside the scale range
(`geom_point()`).
# calculate the standard deviation of both quizzes and summarizesd(df$Pop1)
[1] 1.368476
sd(df$Pop2)
[1] 1.572491
summary(df)
Pop1 Pop2
Min. :5.000 Min. : 6.000
1st Qu.:6.500 1st Qu.: 6.000
Median :8.000 Median : 7.000
Mean :7.455 Mean : 7.545
3rd Qu.:8.500 3rd Qu.: 8.500
Max. :9.000 Max. :10.000
calculate the correlation between the two quizzes
cor(df$Pop1, df$Pop2)
[1] -0.1267369
Also, Canvas calculated the coefficent alpha (Chronbach’s alpha) to be 0.30 for Quiz 1 and 0.31 for Quiz 2.
And I let GitHub CoPilot write a summary (which I have problems with)
“This is a low reliability score, which suggests that the quizzes are not reliable measures of the same construct. This is further supported by the low correlation coefficient of 0.31. This suggests that the quizzes are not measuring the same thing, and that the quizzes are not reliable measures of the same construct.”
