The Scientific Method Assessment Task - Data Analysis Assignment
QUESTION 1 - Single-factor experiments
Use Minitab for this question.
The data in Q1 tab of 60902_AssessmentTask3Data_Spring2018.xlsx records blood cholesterol levels of twenty-eight individuals two and four days after a heart attack.
It is thought that blood cholesterol levels fall progressively in the days after a heart attack. Design tests to determine if cholesterol level falls by more than ten units in the period between two and four days after a heart attack.
(a) Nominate a parametric test and a non-parametric test that could be used in this situation. Identify the main difference [1 mark], contrast the effectiveness and discuss the situations where these tests should be used.
(b) Perform the parametric test identified in part (a) using 0.05 significance level. Write down the null and alternative hypotheses, the test statistic and p-value, the result of the test and your conclusion in non-mathematical language.
(c) Perform the non-parametric test identified in part (a) using 0.05 significance level. Write down the null and alternative hypotheses, the test statistic and p-value, the result of the test and your conclusion in non-mathematical language.
(d) Parametric tests require the sample data to be from certain distributions. Test if this is so in this instance (only test day two sample). Write down the null and alternative hypotheses, the test statistic and p-value, the result of the test and your conclusion in non-mathematical language.
(e) So, does blood cholesterol fall in the days after a heart attack?
QUESTION 2 - Two-factor Experiments
Use Minitab for this question.
The data in Q2 tab of 60902_AssessmentTask3_Data_Spring2018.xlsx records the number of words remembered by individuals (stored as variable words) using the memorising techniques
process ∈ {"adjective", "counting", "imagery", "intentional", "rhyming"}.
The blocking factor
age ∈ {"younger", "older"}
was also employed in the model.
(a) Perform a two-way ANOVA of words using the factors process and age and their interaction. Detail the F-tests on process, age and their interaction using the notation employed in the statistical model of I × J factorial experiments (5 × 2 in this case). Write down the null and alternative hypotheses, the test statistic and p-value, the result of the test and your conclusion in non-mathematical language.
(b) Using appropriate statistical analysis, rank the memorising techniques in order of decreasing effectiveness, ensuring any differences are statistically-significant. Which interaction effect(s) produced the best results for memorisation?
(c) Perform a visual inspection of the standardised residuals, linking each observation with the relevant assumption. Can the conclusions from ANOVA be relied upon in this case?
Question 3 - Simple Linear Regression
Use SPSS for this question.
The data in Q3 tab of 60902_AssessmentTask3Data_Autumn2018.xlsx is a collection of loading (stored as load) and fall velocity (stored as velocity) readings of samara fruit that drop from trees.
(a) Create a scatter plot of loading and velocity and include this chart in your report. Comment on the sign, type and strength of the relationship between the variables.
(b) Construct a simple linear regression model with velocity as response and loading as predictor. Write down the regression equation and provide interpretations of the intercept and slope parameter estimates.
(c) Write down the critical Cook's D for this model. Create a boxplot of Cook's D and determine if there are any influential points.
(d) Perform a test to determine if the true value of the slope parameter is greater than 0.55 (use 0.05 significance). Write down the null and alternative hypotheses, the test statistic and p-value, the result of the test and your conclusion in non-mathematical language.
(e) Perform a visual inspection of the standardised residuals, linking each observation with the relevant assumption. Can the regression model be relied upon in this case?
(f) Describe two ways in which this regression model could be improved.
Attachment:- Data File.rar