advice.Rmd

---
title: Friendly Advice
---

Suggested improvements for Between-subjects t-test (01-201-lab02a).

```{r we, echo = FALSE}
suppressPackageStartupMessages({
  library(tidyverse)
  library(broom)
  library(webexercises) # for round2
})

set.seed(1410)

mx <- runif(1, 0, 100) %>% round2(2)
sdx <- runif(1, 0, 5) %>% round2(2)
N <- seq(10, 100, 2) %>% sample(1)

dat <- tibble(Group = rep(c("A","B"), each = N/2),
              scores = rnorm(N, mx, sdx)) %>%
  mutate(scores = scores + rep(c(0,2), each = N/2))

desc <- dat %>% 
  group_by(Group) %>%
  summarise(Npg = n(),
            Means = mean(scores) %>% round2(2),
            SDs = sd(scores) %>% round2(2),
            Variance = var(scores) %>% round2(2),
            `Standard Err.` = (SDs/sqrt(Npg)) %>% round2(2))

sdp <- sqrt((((N/2 - 1) * desc$SDs[1]^2) + ((N/2 - 1) * desc$SDs[2]^2))/(N/2 + N/2 - 2))

t.value <- ((desc$Means[1] - desc$Means[2])/(sdp * sqrt(((1/(N/2)) + (1/(N/2)))))) %>% round2(2)            

cohensd <- ((2* t.value)/sqrt(N-2)) %>% round2(2)

results <- t.test(dat %>% filter(Group == "A") %>% pull(scores), 
                  dat %>% filter(Group == "B") %>% pull(scores), 
                  var.equal = TRUE) %>% 
  tidy() %>%
  mutate(cohensd_t = (2*statistic)/sqrt(parameter))
```

```{r}
# add this to your script for increased readability and debugging
An <- desc %>% filter(Group == "A") %>% pull(Npg)
Bn <- desc %>% filter(Group == "B") %>% pull(Npg)
Am <- desc %>% filter(Group == "A") %>% pull(Means)
Bm <- desc %>% filter(Group == "B") %>% pull(Means)
Asd <- desc %>% filter(Group == "A") %>% pull(SDs)
Bsd <- desc %>% filter(Group == "B") %>% pull(SDs)

df <- (An - 1) + (Bn - 1)
t_crit <- qt(1-.975, df, lower.tail = FALSE) %>% round2(3)
sd_pooled <- sqrt(((An -1) * Asd * Asd + (Bn -1) * Bsd * Bsd)/(An + Bn - 2)) *
  sqrt((1/(Bn)) + (1/(Bn)))
t_abs <- abs((Am - Bm) / sd_pooled) %>% round2(2)

t_compare <- ifelse(t_abs >= t_crit,  "equal to or larger than",  "smaller than")
t_sig <- ifelse(t_abs >= t_crit, "significant",  "non-significant")
p_val <- ifelse(t_abs >= t_crit, " p < .05", " p > .05")
d <- abs(2 * (Am - Bm) / sd_pooled / sqrt(df)) %>% round2(1)
```


**Determining Significance**

If we were to look at a critical values look-up table for 
$df = `r df`$ and $\alpha = .05$ (two-tailed), 
we would see that the critical value is $t_{crit} = `r t_crit`$. 
Given that our t-value, ignoring polarity and just looking at the absolute value, 
so $t = `r t_abs`$, is `r t_compare` our $t_{crit}$ 
then we can say our result is `r t_sig`, 
and as such would be written up as 
t(`r df`) = `r t_abs`, `r p_val`, d = `r d`.

**is a little easier to read and debug than:**

If we were to look at a critical values look-up table for $df = `r (desc %>% filter(Group == "A") %>% pull(Npg) - 1) + (desc %>% filter(Group == "B") %>% pull(Npg) - 1)`$ and $\alpha = .05$ (two-tailed), we would see that the critical value is $t_{crit} = `r qt(1-.975, (desc %>% filter(Group == "A") %>% pull(Npg) - 1) + (desc %>% filter(Group == "B") %>% pull(Npg) - 1), lower.tail = FALSE) %>% round2(3)`$. Given that our t-value, ignoring polarity and just looking at the absolute value, so $t = `r abs(((desc %>% filter(Group == "A") %>% pull(Means) - desc %>% filter(Group == "B") %>% pull(Means)) / (sqrt(((desc %>% filter(Group == "A") %>% pull(Npg) -1) * desc %>% filter(Group == "A") %>% pull(SDs) * desc %>% filter(Group == "A") %>% pull(SDs) + (desc %>% filter(Group == "B") %>% pull(Npg) -1) * desc %>% filter(Group == "B") %>% pull(SDs) * desc %>% filter(Group == "B") %>% pull(SDs))/(desc %>% filter(Group == "A") %>% pull(Npg) + desc %>% filter(Group == "B") %>% pull(Npg) - 2)) %>% round2(3) * sqrt((1/(desc %>% filter(Group == "B") %>% pull(Npg))) + (1/(desc %>% filter(Group == "B") %>% pull(Npg)))))) %>% round2(2))`$, is `r ifelse(abs(((desc %>% filter(Group == "A") %>% pull(Means) - desc %>% filter(Group == "B") %>% pull(Means)) / (sqrt(((desc %>% filter(Group == "A") %>% pull(Npg) -1) * desc %>% filter(Group == "A") %>% pull(SDs) * desc %>% filter(Group == "A") %>% pull(SDs) + (desc %>% filter(Group == "B") %>% pull(Npg) -1) * desc %>% filter(Group == "B") %>% pull(SDs) * desc %>% filter(Group == "B") %>% pull(SDs))/(desc %>% filter(Group == "A") %>% pull(Npg) + desc %>% filter(Group == "B") %>% pull(Npg) - 2)) %>% round2(3) * sqrt((1/(desc %>% filter(Group == "B") %>% pull(Npg))) + (1/(desc %>% filter(Group == "B") %>% pull(Npg)))))) %>% round2(2)) >= qt(1-.975, (desc %>% filter(Group == "A") %>% pull(Npg) - 1) + (desc %>% filter(Group == "B") %>% pull(Npg) - 1), lower.tail = FALSE), "equal to or larger than", "smaller than")` our $t_{crit}$ then we can say our result is `r ifelse(abs(((desc %>% filter(Group == "A") %>% pull(Means) - desc %>% filter(Group == "B") %>% pull(Means)) / (sqrt(((desc %>% filter(Group == "A") %>% pull(Npg) -1) * desc %>% filter(Group == "A") %>% pull(SDs) * desc %>% filter(Group == "A") %>% pull(SDs) + (desc %>% filter(Group == "B") %>% pull(Npg) -1) * desc %>% filter(Group == "B") %>% pull(SDs) * desc %>% filter(Group == "B") %>% pull(SDs))/(desc %>% filter(Group == "A") %>% pull(Npg) + desc %>% filter(Group == "B") %>% pull(Npg) - 2)) %>% round2(3) * sqrt((1/(desc %>% filter(Group == "B") %>% pull(Npg))) + (1/(desc %>% filter(Group == "B") %>% pull(Npg)))))) %>% round2(2)) >= qt(1-.975, (desc %>% filter(Group == "A") %>% pull(Npg) - 1) + (desc %>% filter(Group == "B") %>% pull(Npg) - 1), lower.tail = FALSE), "significant", "non-significant")`, and as such would be written up as t(`r (desc %>% filter(Group == "A") %>% pull(Npg) - 1) + (desc %>% filter(Group == "B") %>% pull(Npg) - 1)`) = `r abs(((desc %>% filter(Group == "A") %>% pull(Means) - desc %>% filter(Group == "B") %>% pull(Means)) / (sqrt(((desc %>% filter(Group == "A") %>% pull(Npg) -1) * desc %>% filter(Group == "A") %>% pull(SDs) * desc %>% filter(Group == "A") %>% pull(SDs) + (desc %>% filter(Group == "B") %>% pull(Npg) -1) * desc %>% filter(Group == "B") %>% pull(SDs) * desc %>% filter(Group == "B") %>% pull(SDs))/(desc %>% filter(Group == "A") %>% pull(Npg) + desc %>% filter(Group == "B") %>% pull(Npg) - 2)) %>% round2(3) * sqrt((1/(desc %>% filter(Group == "B") %>% pull(Npg))) + (1/(desc %>% filter(Group == "B") %>% pull(Npg)))))) %>% round2(2))`,`r ifelse(abs(((desc %>% filter(Group == "A") %>% pull(Means) - desc %>% filter(Group == "B") %>% pull(Means)) / (sqrt(((desc %>% filter(Group == "A") %>% pull(Npg) -1) * desc %>% filter(Group == "A") %>% pull(SDs) * desc %>% filter(Group == "A") %>% pull(SDs) + (desc %>% filter(Group == "B") %>% pull(Npg) -1) * desc %>% filter(Group == "B") %>% pull(SDs) * desc %>% filter(Group == "B") %>% pull(SDs))/(desc %>% filter(Group == "A") %>% pull(Npg) + desc %>% filter(Group == "B") %>% pull(Npg) - 2)) %>% round2(3) * sqrt((1/(desc %>% filter(Group == "B") %>% pull(Npg))) + (1/(desc %>% filter(Group == "B") %>% pull(Npg)))))) %>% round2(2)) >= qt(1-.975, (desc %>% filter(Group == "A") %>% pull(Npg) - 1) + (desc %>% filter(Group == "B") %>% pull(Npg) - 1), lower.tail = FALSE), " p < .05", " p > .05")`, d = `r abs(((2 * ((desc %>% filter(Group == "A") %>% pull(Means) - desc %>% filter(Group == "B") %>% pull(Means)) / (sqrt(((desc %>% filter(Group == "A") %>% pull(Npg) -1) * desc %>% filter(Group == "A") %>% pull(SDs) * desc %>% filter(Group == "A") %>% pull(SDs) + (desc %>% filter(Group == "B") %>% pull(Npg) -1) * desc %>% filter(Group == "B") %>% pull(SDs) * desc %>% filter(Group == "B") %>% pull(SDs))/(desc %>% filter(Group == "A") %>% pull(Npg) + desc %>% filter(Group == "B") %>% pull(Npg) - 2)) %>% round2(3) * sqrt((1/(desc %>% filter(Group == "B") %>% pull(Npg))) + (1/(desc %>% filter(Group == "B") %>% pull(Npg)))))) %>% round2(2)) / (sqrt((desc %>% filter(Group == "A") %>% pull(Npg) - 1) + (desc %>% filter(Group == "B") %>% pull(Npg) - 1)))) %>% round2(2))`

### Lookup Table

```{r, results='asis'}
# the manual lookup table could be replaced with this

tibble(df = c(1:10, 15, seq(20, 100, 10))) %>%
  mutate(alpha = map_dbl(df, ~qt(1-.975, .x, lower.tail = FALSE)),
         alpha = round2(alpha, 3)) %>%
  knitr::kable(digits = 3, col.names = c("df", "$\\alpha = .05$"))
```