Statistics Assignment: Hypothesis Testing, ANOVA, and Regression

This document presents solutions to a statistics homework assignment. The assignment covers key statistical concepts including the interpretation of standard error bars, correlation versus causation, and the relationship between F-values and p-values in linear regression. It also includes calculations and interpretations related to ANOVA, such as determining the F-value and understanding degrees of freedom. The solutions address questions on interaction plots, post-hoc tests like LSD, and the assumptions underlying statistical analyses. Furthermore, it provides insights into the appropriate use of t-tests, multiple linear regression, and other statistical methods, along with the impact of model term order on p-values. This resource is designed to help students understand and apply statistical principles effectively.

1)
Standard error bar are used for analysing the spread of the data around the mean value.
Ans)
 The confidence in the mean values of different groups
2) Correlated will be the one which will affect the other. In this case the temperature if it is more ice
creams sold will be also more and the vice versa
Ans)
 The temperature and the number of ice-creams consumed on a given day in Perth.
 The amount of sunscreen used and the number of ice-creams consumed on a given day in
Perth.
 The amount of heating used and temperature on a given day in Perth.
 The amount of sunscreen used and the amount of heating used on a given day in Perth.
3) Magnitude of the slope has nothing to do with the p value of the estimated slope
Ans)
 For a simple linear regression, a higher F value always means a lower p-value.
 For a simple linear regression, a higher slope coefficient never means a lower p-value.
4)
Mean Square of residuals = (sum of squares)/ Degrees of Freedom = 1.5837/12 = 0.131975
Means square error of treatments = 5.3371
F – value = (MST/MSE) = (5.3371/0.131975) = 40.440
Ans)
 40.440
5) Degrees of freedom determines thee F value
Ans)
 It depends on what the degrees of freedom actually are
6)
Ans)
 The way that the effect of N on wheat yield depends on the P level, is different for
different varieties
 The way that the effect of P on wheat yield depends on the N level, is different for
different varieties
 The effect of P on wheat yield depends on the N level and also on variety
7)
Ans)

 Interpret it using an interaction plot or table and then draw additional conclusions based
on the significance of the main effects
8)
Ans)
 The probability of obtaining a significant result from the analysis, given a certain effect
size, and given all the assumptions are true
 The mean sum of squares for the variance explained by a factor, divided by the mean sum
of squares for the unexplained variance
 The probability that the null hypothesis is true
 The probability that an F value at least as big as that observed would have been obtained
if the null hypothesis and other assumptions were true
9)
Ans)
 After the ANOVA is performed, if the ANOVA is significant, to get extra information
10)
Ans)
 Least Significant Difference
11)
Ans)
 Pairwise t.test based on pooled variance (LSD) (Least strict or conservative)
 Tukey Honest Significant Difference (In the middle)
 Bonferroni test (Most strict or conservative)
12)
Ans)
 T-test with assumed
equal variances
 Multiple linear regression
 One-way ANOVA
 Simple linear regression
 Proportion test
13)
Ans)

 The means in the groups (treatments) are equal.
 The means of the groups are normally distributed.
 The measurements in different groups do not depend on each other.
 All the measured values are normally distributed.
14)
Ans)
 if the lines in the interaction plot are clearly NOT parallel
 if one line in the interaction plot is approximately horizontal, and the other goes up at a
steep slope
 if the lines in the interaction plot are approximately parallel, but still just cross
 if one line in the interaction plot goes down at a steep slope, and the other goes up at a
steep slope
 if the lines in the interaction plot are approximately, but not exactly, parallel
15)
Ans)
 t-tests are used to get the p-values that you see
 the order of the model terms makes a difference to the p-values obtained if the data come
from a fully replicated full factorial experiment (ie explanatory variables are orthogonal)
 the order of the model terms always makes a difference to the p-values obtained