How to Read a Latin Squares Main Effects Plot
Latin Squares, Graeco-Latin Squares, & Factorial experiments
Evaluate the NYC Sabbatum scores data and deal with its missing values, then evaluate Latin Foursquare, Graeco-Latin Foursquare, and Factorial experiments.
Latin Squares Video
NYC Sabbatum Scores EDA
Math is a subject the U.Southward. is consistently behind the rest of the world on, and so our experiments will focus on Math score. While the original dataset is an open dataset downloaded from Kaggle, throughout this chapter I volition add together a few variables that will allow you to pretend y'all are an education researcher conducting experiments ideally aimed at raising students' scores, hopefully increasing the likelihood they will be admitted to colleges.
Before diving into analyzing the experiments, we should do some EDA to brand sure we fully sympathize the nyc_scores data. In this lesson, we'll do experiments where we block by Borough and Teacher_Education_Level, so let'due south examine math scores by those variables. The nyc_scores dataset has been loaded for you lot.
Exercise
- Observe the mean, variance, and median of
Average_Score_SAT_MathbyBoroughusingdplyrmethods for EDA as nosotros have used them throughout the course.
# Mean, var, and median of Math score nyc_scores %>% group_by(Borough) %>% summarize(mean = mean(Average_Score_SAT_Math, na.rm = True), var = var(Average_Score_SAT_Math, na.rm = TRUE), median = median(Average_Score_SAT_Math, na.rm = TRUE)) # A tibble: 5 x 4 Civic mean var median <fct> <dbl> <dbl> <dbl> 1 Bronx 404. 2727. 396. 2 Brooklyn 416. 3658. 395 3 Manhattan 456. 7026. 433 4 Queens 462. 5168. 448 5 Staten Isle 486. 6911. 466. - Detect the mean, variance, and median of
Average_Score_SAT_MathbyTeacher_Education_LevelusingdplyrEDA methods.
# Mean, var, and median of Math score by Teacher Instruction Level nyc_scores %>% group_by(Teacher_Education_Level) %>% summarize(mean = mean(Average_Score_SAT_Math, na.rm = Truthful), var = var(Average_Score_SAT_Math, na.rm = TRUE), median = median(Average_Score_SAT_Math, na.rm = TRUE)) # A tibble: 5 x 4 Teacher_Education_Level mean var median <fct> <dbl> <dbl> <dbl> 1 BA 427. 4114. 415 2 College Student 423. 4043. 410. 3 Grad Student 430. 4694. 416. four MA 449. 6520. 418. five PhD 432. 6654. 408 - Observe the hateful, variance, and median of
Average_Score_SAT_Mathby bothCivicandTeacher_Education_LevelusingdplyrEDA methods.
# Hateful, var, and median of Math score past both nyc_scores %>% group_by(Civic, Teacher_Education_Level) %>% summarize(mean = hateful(Average_Score_SAT_Math, na.rm = True), var = var(Average_Score_SAT_Math, na.rm = TRUE), median = median(Average_Score_SAT_Math, na.rm = TRUE)) # A tibble: 25 x five # Groups: Borough [5] Borough Teacher_Education_Level mean var median <fct> <fct> <dbl> <dbl> <dbl> 1 Bronx BA 394. 1458. 383 2 Bronx Higher Pupil 401. 1291. 390 3 Bronx Grad Student 403. 1274. 402. four Bronx MA 418. 6047. 400. 5 Bronx PhD 390. 621. 393 6 Brooklyn BA 416. 2335. 394 7 Brooklyn Higher Student 432. 5811. 420 8 Brooklyn Grad Pupil 401. 1988. 394 9 Brooklyn MA 434. 4955. 408 ten Brooklyn PhD 388. 2033. 380 # … with 15 more rows At present that nosotros've examined the data, we can move on to cleaning it, the next important step earlier analysis.
Dealing with Missing Exam Scores
If we desire to use Sat scores as our outcome, we should examine missingness. Examine the pattern of missingness across all the variables in nyc_scores using miss_var_summary() from the naniar packet written by Tierney et al. (2019). naniar integrates with Tidyverse code styling, including the pipe operator (%>%).
There are threescore missing scores in each field of study. Though in that location are many R packages which assistance with more advanced forms of imputation, such as MICE, Amelia, and mi, we will continue to utilise simputation and impute_median().
Create a new dataset, nyc_scores_2 by imputing Math score by Borough, but note that impute_median() returns the imputed variable equally blazon "impute". Y'all'll convert the variable to the numeric in a separate step.
simputation and dplyr are loaded.
Exercise
- Load the `naniar packet.
# Load naniar library(naniar) Attaching package: 'naniar' The post-obit object is masked from 'packet:simputation': impute_median - Examine the missingness of variables in
nyc_scorespast piping it tomiss_var_summary().
# Examine missingness with miss_var_summary() nyc_scores %>% miss_var_summary() # A tibble: 23 ten iii variable n_miss pct_miss <chr> <int> <dbl> 1 Average_Score_SAT_Math 60 xiii.8 2 Average_Score_SAT_Reading 60 13.8 3 Average_Score_SAT_Writing lx thirteen.8 four Percent_Tested 49 11.3 five Student_Enrollment 7 1.61 6 Percent_White 7 one.61 vii Percent_Black seven 1.61 8 Percent_Hispanic seven 1.61 9 Percent_Asian vii 1.61 10 School_ID 0 0 # … with 13 more rows - Create
nyc_scores_2by imputing the Math score by Borough (nosotros're only using Math in our experiments.)
# Examine missingness with md.blueprint()---from mice package! mice:: physician.pattern(nyc_scores) 
School_ID School_Name Civic Building_Code Street_Address City Land 375 1 1 1 1 1 i i xi 1 1 1 ane 1 1 1 42 1 1 1 1 1 1 1 7 1 1 1 ane 1 1 1 0 0 0 0 0 0 0 Zip_Code Latitude Longitude Phone_Number Start_Time End_Time 375 one 1 1 1 1 1 eleven 1 1 1 1 i 1 42 1 1 ane 1 i one seven 1 1 i i i 1 0 0 0 0 0 0 Teacher_Education_Level Student_Enrollment Percent_White Percent_Black 375 one one 1 1 11 1 1 ane 1 42 1 1 1 1 vii 1 0 0 0 0 7 7 7 Percent_Hispanic Percent_Asian Percent_Tested Average_Score_SAT_Math 375 1 1 1 i 11 ane 1 i 0 42 1 1 0 0 vii 0 0 0 0 seven seven 49 threescore Average_Score_SAT_Reading Average_Score_SAT_Writing 375 1 1 0 xi 0 0 iii 42 0 0 four 7 0 0 9 threescore lx 264 library(simputation) # Impute the Math score past Civic # Note loading nanier masks the impute_median function from # simputation....so must specify the package!!!! nyc_scores_ii <- simputation:: impute_median(nyc_scores, Average_Score_SAT_Math ~ Borough) - Catechumen
nyc_scores_2$Average_Score_SAT_Mathto numeric.
# Convert Math score to numeric nyc_scores_2 $Average_Score_SAT_Math <- as.numeric(nyc_scores_2 $Average_Score_SAT_Math) - Use
dplyrto examine the median and mean of math score before and after imputation.
# Examine scores by Borough in both datasets, before and later on imputation nyc_scores %>% group_by(Borough) %>% summarize(median = median(Average_Score_SAT_Math, na.rm = TRUE), hateful = mean(Average_Score_SAT_Math, na.rm = TRUE)) # A tibble: five x 3 Borough median mean <fct> <dbl> <dbl> i Bronx 396. 404. two Brooklyn 395 416. 3 Manhattan 433 456. four Queens 448 462. v Staten Isle 466. 486. nyc_scores_2 %>% group_by(Borough) %>% summarize(median = median(Average_Score_SAT_Math, na.rm = TRUE), mean = mean(Average_Score_SAT_Math, na.rm = Truthful)) # A tibble: 5 x 3 Civic median mean <fct> <dbl> <dbl> 1 Bronx 396. 403. 2 Brooklyn 395 414. three Manhattan 433 452. four Queens 448 460. 5 Staten Island 466. 486. Did the median scores change before and afterwards imputation? (Hint: they shouldn't have changed past much, simply rounding may have offset them by an integer or 2.)
Cartoon Latin Squares with agricolae
Nosotros return, once again, to the agricolae package to examine what a Latin Square pattern tin can wait like. Hither'south an instance:
[,ane] [,2] [,three] [,4] [i,] "A" "C" "D" "B" [2,] "D" "B" "C" "A" [3,] "B" "D" "A" "C" [4,] "C" "A" "B" "D" Since a Latin Foursquare experiment has two blocking factors, you can encounter that in this pattern, each handling appears once in both each row (blocking factor 1) and each column (blocking factor 2).
Look at the help page for blueprint.lsd() by typing ?blueprint.lsd in the console for any assist yous need designing your Latin Square experiment.
- Load the
agricolaepacket.
# Load agricolae library(agricolae) - Create and view the sketch of a Latin Square design,
my_design_lsd, using treatments A, B, C, D, & Eastward, and a seed of 42.
# Design a LS with 5 treatments A:E then look at the sketch my_design_lsd <- pattern.lsd(Messages[1 : 5], seed = 42) my_design_lsd$sketch [,ane] [,2] [,3] [,4] [,5] [i,] "B" "E" "D" "A" "C" [2,] "A" "D" "C" "E" "B" [iii,] "E" "C" "B" "D" "A" [iv,] "C" "A" "Eastward" "B" "D" [v,] "D" "B" "A" "C" "Eastward" Possibly yous're thinking to yourself… This looks a lot like a RCBD … It does, only equally nosotros know from the video, there are now two blocking factors in a LS design.
Latin Square with NYC Sat Scores
To execute a Latin Square design on this data, suppose we want to know the result of our tutoring program, which includes 1-on-1 tutoring, two small groups, and an in and later on-school SAT prep class. A new dataset nyc_scores_ls is available that represents this experiment. Feel free to explore the dataset in the console.
Nosotros'll block past Borough and Teacher_Education_Level to reduce their known variance on the score outcome. Borough is a skilful blocking gene because schools in America are funded partly based on taxes paid in each city, so it will likely make a deviation in the quality of education.
Exercise
- Use
lm()to exam the changes inAverage_Score_SAT_Mathusingnyc_scores_ls.
# Build nyc_scores_ls_lm nyc_scores_ls_lm <- lm(Average_Score_SAT_Math ~ Tutoring_Program + Borough + Teacher_Education_Level, information = nyc_scores_ls ) - Tidy
nyc_scores_ls_lmwith the appropriatebroomfunction.
# Tidy the results with broom broom:: tidy(nyc_scores_ls_lm) # A tibble: thirteen x v term guess std.fault statistic p.value <chr> <dbl> <dbl> <dbl> <dbl> 1 (Intercept) 413. 64.0 6.45 three.14e-5 2 Tutoring_ProgramSAT Prep Form (a… -54.4 61.0 -0.892 iii.90e-ane 3 Tutoring_ProgramSAT Prep Class (southward… -30.9 64.4 -0.480 6.40e-1 4 Tutoring_ProgramSmall Groups (2-iii) 0.417 60.4 0.00690 9.95e-ane v Tutoring_ProgramSmall Groups (four-6) -36.0 58.1 -0.619 5.47e-1 6 BoroughBrooklyn 55.0 53.6 1.03 three.24e-1 7 BoroughManhattan 21.9 45.4 0.482 six.39e-1 8 BoroughQueens 46.0 53.6 0.858 4.08e-1 9 BoroughStaten Island 352. 89.9 3.91 2.05e-3 10 Teacher_Education_LevelCollege St… 7.thirty 52.1 0.140 8.91e-1 11 Teacher_Education_LevelGrad Stude… 72.4 46.v 1.56 1.45e-1 12 Teacher_Education_LevelMA 36.6 47.6 0.768 4.57e-1 13 Teacher_Education_LevelPhD 113. 59.3 1.91 8.04e-2 - Examine
nyc_scores_ls_lmwithanova().
# Examine the results with anova anova(nyc_scores_ls_lm) Analysis of Variance Table Response: Average_Score_SAT_Math Df Sum Sq Mean Sq F value Pr(>F) Tutoring_Program 4 19238 4809.four 0.9087 0.48959 Borough four 78483 19620.vii 3.7071 0.03457 * Teacher_Education_Level 4 26884 6721.0 ane.2698 0.33496 Residuals 12 63514 5292.viii --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Question At the 0.05 significance level, practice we have bear witness to believe the tutoring programme has an consequence on math SAT scores, when blocked by Borough and Teacher_Education_Level?
-
Nope! Given the p-value (0.2261), nosotros have no reason to reject the nothing hypothesis.
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Yes! Given the p-value (0.2261), we have reason to believe that the tutoring plan had an effect on the Math score.
It seems that when nosotros block for Civic of the school and Teacher_Education_Level, our Tutoring_Program isn't having a statistically meaning effect on the Math Sabbatum score.
Graeco-Latin Squares Video
NYC Sat Scores Data Viz
In the concluding lesson, when discussing Latin Squares, nosotros did numerical EDA in the course of looking at means, variances, and medians of the math SAT scores. Some other crucial part of the EDA is data visualization, as it ofttimes helps in spotting outliers plus gives yous a visual representation of the distribution of your variables.
ggplot2 has been loaded for you lot and the nyc_scores dataset is bachelor. Create and examine the requested boxplot. How practise the medians differ past Civic? How many outliers are nowadays, and where are they more often than not present?
Practise
- Create a boxplot of Math Saturday scores by
Civic.
library(ggplot2) ggplot(data = nyc_scores, aes(x = Borough, y = Average_Score_SAT_Math)) + geom_boxplot() Warning: Removed 60 rows containing non-finite values (stat_boxplot). 
- Run the lawmaking to include a title: "Boilerplate SAT Math Scores by Borough, NYC".
ggplot(information = nyc_scores, aes(ten = Borough, y = Average_Score_SAT_Math)) + geom_boxplot() + ggtitle("Average SAT Math Scores by Borough, NYC") Alarm: Removed lx rows containing non-finite values (stat_boxplot). 
- Change the x- and y-axis labels to read
"Borough (NYC)"and"Average SAT Math Scores (2014-15)", respectively, using the correct arguments tolabs().
ggplot(data = nyc_scores, aes(ten = Borough, y = Average_Score_SAT_Math)) + geom_boxplot() + ggtitle("Boilerplate Saturday Math Scores by Civic, NYC") + labs(xlab("Borough (NYC)") , ylab("Average SAT Math Scores (2014-xv)")) Alarm: Removed 60 rows containing non-finite values (stat_boxplot). 
## or ggplot(data = nyc_scores, aes(10 = Borough, y = Average_Score_SAT_Math)) + geom_boxplot() + labs(championship = "Average Sat Math Scores by Borough, NYC", x = "Civic (NYC)", y = "Average Sat Math Scores (2014-15)") + theme_bw() Warning: Removed 60 rows containing non-finite values (stat_boxplot). 
It's interesting to run across the unlike distribution of scores past Civic and to see that every civic has scores that are outliers, though some more than than others.
Drawing Graeco-Latin Squares with agricolae
As we've seen, agricolae provides united states of america the power to draw all of the experimental designs we've used so far, and they can besides depict Graeco-Latin squares. Ane difference in the input to design.graeco() that we haven't seen earlier is that we'll need to input 2 vectors, trt1 and trt2, which must be of equal length. Y'all can call up of trt1 equally your bodily treatment and trt2 as one of your blocking factors. agricolae has been loaded for yous.
Practice
- Create vectors
trt1withLETTERSA through E andtrt2with numbers 1 through 5.
# Create trt1 and trt2 trt1 <- Letters[1 : 5] trt2 <- 1 : 5 - Brand
my_graeco_designwithblueprint.graeco(), using andseed = 42.
# Create my_graeco_design my_graeco_design <- design.graeco(trt1, trt2, seed = 42) - Examine the
parametersandsketchofmy_graeco_design.
# Examine the parameters and sketch my_graeco_design$parameters $design [1] "graeco" $trt1 [i] "A" "B" "C" "D" "Eastward" $trt2 [one] ane ii 3 4 5 $r [ane] v $serie [one] 2 $seed [1] 42 $kinds [1] "Super-Duper" [[8]] [i] TRUE [,one] [,2] [,3] [,4] [,5] [1,] "D 2" "E 3" "A 1" "C 5" "B 4" [2,] "E 1" "A 5" "C iv" "B 2" "D 3" [iii,] "A 4" "C two" "B 3" "D 1" "E 5" [4,] "C 3" "B i" "D 5" "E 4" "A two" [five,] "B five" "D 4" "E two" "A three" "C 1" Yous tin run across that this time the sketch object includes your handling (the capital letter) and a blocking factor (the number.)
Graeco-Latin Square with NYC Saturday Scores
Recall that our Latin Foursquare exercise in this chapter tested the effect of our tutoring programme, blocked by Civic and Teacher_Education_Level.
For our Graeco-Latin Square, say we also want to block out the known effect of Homework_Type, which indicates what kind of homework the student was given: individual merely, small or large group homework, or some combination. We tin can add this as another blocking gene to create a Graeco-Latin Square experiment.
Do
- Utilize
lm()to test the changes inAverage_Score_SAT_Mathusing thenyc_scores_glsdata.
# Build nyc_scores_gls_lm nyc_scores_gls_lm <- lm(Average_Score_SAT_Math ~ Tutoring_Program + Borough + Teacher_Education_Level + Homework_Type, information = nyc_scores_gls) - Tidy
nyc_scores_gls_lmwith the appropriatebroomfunction.
# Tidy the results with broom broom:: tidy(nyc_scores_gls_lm) # A tibble: 17 x five term estimate std.error statistic p.value <chr> <dbl> <dbl> <dbl> <dbl> 1 (Intercept) 405. lxxx.iv 5.03 0.00102 2 Tutoring_ProgramSAT Prep Course (af… -47.2 69.0 -0.684 0.513 3 Tutoring_ProgramSAT Prep Form (sc… 33.2 80.3 0.414 0.690 4 Tutoring_ProgramSmall Groups (2-iii) 4.02 75.half dozen 0.0531 0.959 5 Tutoring_ProgramSmall Groups (iv-six) -29.7 64.five -0.461 0.657 6 BoroughBrooklyn 33.ii 75.iii 0.441 0.671 7 BoroughManhattan 35.6 51.0 0.697 0.505 eight BoroughQueens 93.5 66.ix i.40 0.200 ix BoroughStaten Island 300. 107. 2.81 0.0229 ten Teacher_Education_LevelCollege Stu… 17.0 67.2 0.252 0.807 11 Teacher_Education_LevelGrad Student 54.0 63.vi 0.849 0.421 12 Teacher_Education_LevelMA 15.iv 55.7 0.276 0.789 13 Teacher_Education_LevelPhD 133. 72.3 i.84 0.104 14 Homework_TypeLarge Group 53.4 seventy.5 0.757 0.471 15 Homework_TypeMix of Large Group/In… -49.8 69.4 -0.717 0.494 16 Homework_TypeMix of Minor Group/In… -38.7 58.8 -0.659 0.529 17 Homework_TypeSmall Group -47.5 62.9 -0.756 0.472 - Examine
nyc_scores_gls_lmwithanova().
# Examine the results with anova anova(nyc_scores_gls_lm) Analysis of Variance Table Response: Average_Score_SAT_Math Df Sum Sq Hateful Sq F value Pr(>F) Tutoring_Program 4 19238 4809.4 0.8277 0.54329 Borough four 78483 19620.7 3.3765 0.06725 . Teacher_Education_Level 4 26884 6721.0 ane.1566 0.39734 Homework_Type iv 17026 4256.5 0.7325 0.59474 Residuals 8 46487 5810.9 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Question
At the 0.05 significance level, exercise we take evidence to believe the tutoring program has an effect on math SAT scores, when blocked by Borough, Teacher_Education_Level, and Homework_Type?
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Nope! Given the p-value, we have no reason to reject the null hypothesis.
-
Yes! Given the p-value, we have reason to believe that the tutoring program had an event on the Math score.
It seems that here, when blocked out past all the other factors, our Tutoring programme has no effect on the Math score.
Factorial Experiments Video
NYC SAT Scores Factorial EDA
Permit's do some more EDA earlier we dive into the analysis of our factorial experiment.
Let's examination the effect of Percent_Black_HL, Percent_Tested_HL, and Tutoring_Program on the effect, Average_Score_SAT_Math. The HL stands for loftier-low, where a one indicates respectively that less than 50% of Blackness students or that less than l% of all students in an entire schoolhouse were tested, and a 2 indicates that greater than l% of either were tested.
Build a boxplot of each factor vs. the outcome to have an idea of which have a difference in median by factor level (ultimately, mean difference is what'due south tested.) The nyc_scores dataset has been loaded for you.
Exercise
- Load
ggplot2. Create a boxplot of the outcome versusTutoring_Program.
# More made upward information nyc_scores$Tutoring_Program <- rep(c("Yep", "No"), supersede = Truthful, length = 435) # Load ggplot2 library(ggplot2) # Build the boxplot for the tutoring programme vs. Math SAT score ggplot(data = nyc_scores, aes(Tutoring_Program, Average_Score_SAT_Math)) + geom_boxplot() + theme_bw() Warning: Removed 60 rows containing not-finite values (stat_boxplot). 
- Using
ggplot2, create a boxplot of the issue versusPercent_Black_HL.
# Feature engineering Percent_Black_HL <- factor(ifelse(nyc_scores$Percent_Black < 0.5, one, 2)) Percent_Tested_HL <- factor(ifelse(nyc_scores$Percent_Tested < 0.5, 1, 2)) nyc_scores$Percent_Black_HL <- Percent_Black_HL nyc_scores$Percent_Tested_HL <- Percent_Tested_HL rm("Percent_Tested_HL", "Percent_Black_HL") # Build the boxplot for the pct black vs. Math Saturday score ggplot(data = nyc_scores, aes(x = Percent_Black_HL, y = Average_Score_SAT_Math)) + geom_boxplot() Warning: Removed 60 rows containing non-finite values (stat_boxplot). 
- Using
ggplot2, create a boxplot of the consequence versusPercent_Tested_HL.
# Build the boxplot for percent tested vs. Math SAT score ggplot(information = nyc_scores, aes(10 = Percent_Tested_HL, y = Average_Score_SAT_Math)) + geom_boxplot() Warning: Removed sixty rows containing non-finite values (stat_boxplot). 
Factorial Experiment with NYC SAT Scores
Now we want to examine the consequence of tutoring programs on the NYC schools' Sat Math score. As noted in the last exercise: the variable Tutoring_Program is just yes or no, depending on if a school got a tutoring programme implemented. For Percent_Black_HL and Percent_Tested_HL, HL stands for high/low. A i indicates less than 50% Black students or overall students tested, and a 2 indicates greater than 50% of both.
Remember that because nosotros intend to test all of the possible combinations of factor levels, we need to write the formula like:
outcome ~ factor1 * factor2 * factor3 Exercise
-
Utilize
aov()to create a model to test howPercent_Tested_HL,Percent_Black_HL, andTutoring_Programbear upon the issueAverage_Score_SAT_Math. -
Salvage the outcome as a model object,
nyc_scores_factorial, and examine this withtidy().
# Create nyc_scores_factorial and examine the results nyc_scores_factorial <- aov(Average_Score_SAT_Math ~ Percent_Tested_HL*Percent_Black_HL*Tutoring_Program, information = nyc_scores) broom:: tidy(nyc_scores_factorial) # A tibble: eight x 6 term df sumsq meansq statistic p.value <chr> <dbl> <dbl> <dbl> <dbl> <dbl> 1 Percent_Tested_HL 1 1.90e5 1.90e5 43.7 1.35e-ten 2 Percent_Black_HL one 1.09e5 1.09e5 25.0 9.07e- seven three Tutoring_Program ane 6.03e3 6.03e3 1.39 2.40e- 1 iv Percent_Tested_HL:Percent_Blac… 1 3.29e4 3.29e4 seven.57 6.23e- iii 5 Percent_Tested_HL:Tutoring_Pro… 1 2.19e1 2.19e1 0.00504 9.43e- 1 6 Percent_Black_HL:Tutoring_Prog… 1 2.30e1 2.30e1 0.00528 9.42e- 1 vii Percent_Tested_HL:Percent_Blac… ane 1.58e3 one.58e3 0.362 5.48e- ane 8 Residuals 367 1.60e6 4.35e3 NA NA Check the circumlocution on datacamp here every bit information technology makes little to no sense…
Evaluating the NYC SAT Scores Factorial Model
We've built our model, so we know what'southward next: model checking! We demand to examine both if our outcome and our model residuals are unremarkably distributed. We'll check the normality assumption using shapiro.examination(). A low p-value means we can reject the cipher hypothesis that the sample came from a normally distributed population.
Let'southward carry out the requisite model checks for our \(two^k\) factorial model, nyc_scores_factorial, which has been loaded for you.
Exercise
- Examination the result
Average_Score_SAT_Mathfromnyc_scoresfor normality usingshapiro.test().
# Use shapiro.exam() to test the issue shapiro.examination(nyc_scores$Average_Score_SAT_Math) Shapiro-Wilk normality examination data: nyc_scores$Average_Score_SAT_Math W = 0.84672, p-value < 2.2e-16 - Set a ii by 2 grid for plots and plot the
nyc_scores_factorialmodel object to create the remainder plots.
# Plot nyc_scores_factorial to examine residuals par(mfrow = c(2,2)) plot(nyc_scores_factorial) 
In that location are bug with this model!
What's side by side in Experimental Design Video
References
Source: https://stat-ata-asu.github.io/ExperimentalDesignInR/latin-squares-graeco-latin-squares-factorial-experiments.html
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