Update inference-many-means.qmd

inference-many-means.qmd

@@ -86,7 +86,7 @@ Investigating groups IV, V, and VI, we see the differences in the groups' center
 #|   Two sets of side by side dot plots. The first set shows three
 #|   groups of observations where the variability within a group is so large
 #|   that it swamps out any variability across the groups. The second set
-#|   shows three groups of observations where the variabilit within a group is
+#|   shows three groups of observations where the variability within a group is
 #|   much smaller and the center of the groups appears different.
 #| fig-asp: 0.5
 toy_anova |>
@@ -385,7 +385,7 @@ classdata |>
 #| label: fig-boxplotThreeVersionsOfExams
 #| fig-cap: Exam scores for students given one of three different exams.
 #| fig-alt: |
-#|   Side-by-side box plots of exam score boken down by exam A, exam B, or
+#|   Side-by-side box plots of exam score broken down by exam A, exam B, or
 #|   exam C. Exam C's median is above 80 which is higher than exam A with a median
 #|   around 74 and exam B with a median around 72.
 classdata |>
@@ -507,7 +507,7 @@ While it is temping to say that exam C is harder than the other two (given the i
 When the null hypothesis is true, random variability that exists in nature sometimes produces data with p-values less than 0.05.
 How often does that happen?
 5% of the time.
-That is to say, if you use 20 different models applied to the same data where there is no signal (i.e., the null hypothesis is true), you are reasonably likely to to get a p-value less than 0.05 in one of the tests you run.
+That is to say, if you use 20 different models applied to the same data where there is no signal (i.e., the null hypothesis is true), you are reasonably likely to get a p-value less than 0.05 in one of the tests you run.
 The details surrounding the ideas of this problem, called a **multiple comparisons test** or **multiple comparisons problem**, are outside the scope of this textbook, but should be something that you keep in the back of your head.
 To best mitigate any extra Type I errors, we suggest that you set up your hypotheses and testing protocol before running any analyses.
 Once the conclusions have been reached, you should report your findings instead of running a different type of test on the same data.
@@ -536,7 +536,7 @@ If $H_0$ is true and the model conditions are satisfied, an $F$-statistic follow
 :::
 
 ::: {.guidedpractice data-latex=""}
-For the baseball data, $MSG = 0.00803$ and $MSE=0.00158.$ Identify the degrees of freedom associated with MSG and MSE and verify the $F$-statistic is approximately 5.077.[^22-inference-many-means-5]
+For the baseball data, $MSG = 0.00803$ and $MSE=0.00158$. Identify the degrees of freedom associated with MSG and MSE and verify the $F$-statistic is approximately 5.077.[^22-inference-many-means-5]
 :::
 
 [^22-inference-many-means-5]: There are $k = 3$ groups, so $df_{G} = k - 1 = 2.$ There are $n = n_1 + n_2 + n_3 = 429$ total observations, so $df_{E} = n - k = 426.$ Then the $F$-statistic is computed as the ratio of $MSG$ and $MSE:$ $F = \frac{MSG}{MSE} = \frac{0.00803}{0.00158} = 5.082 \approx 5.077.$ $(F = 5.077$ was computed by using values for $MSG$ and $MSE$ that were not rounded.)