Statistics Assignment

1. Clonogenic Assay

Attached is an Excel file with data from Clonogenic Assay. 3 cell lines are treated for 48 hours with 3 drugs (Etopside, 5FU & Oxaliplatin) at 4 concentrations \((0,1, .2, .04 \mu \mathrm{M})\). Clonogenic ability was assessed by plating 100 cells in \(6 \mathrm{~cm}\) dishes. After 14 days the colonies that have grown are fixed, stained and the number of colonies counted in triplicate dishes. The whole experiment was repeated for 3 times for each cell line/drug/concentration. Data from contaminated wells were discarded. The primary research question/objective was whether all the three drugs have equal cytotoxic effect or not. The secondary objective was whether the efficacy of the drugs varied in terms of the concentrations used.

The data file is also available in the QMPlus as an SPSS file "Assignment_clonogenic assay.sav".

1. Categorise the variables cell line, drug, concentration and number of colonies as binary, nominal, ordinal, discrete and continuous with appropriate reason.
2. Summarise the sample data in terms of the primary and the secondary research questions/objectives using descriptive statistics. First you will need to use an appropriate plot to compare the distribution of the variables of interest (describe the key findings from the plot). Then also use one measure from average and one measure from spread to summarise them numerically (comment on the measures). Be precise and specific and don't provide all output data from SPSS (ie do not provide unnecessary information). Follow the style of published research articles where sample data is summarised before applying any inferential statistics.
3. Test the hypothesis that the cytotoxic effects of drug Etoposide, \(5 \mathrm{FU}\) and Oxaliplatin on cells' clonogenic ability are not equal. Check the assumptions of your test before you apply it. If your test shows that their effects are not equal, then test which drug's effect differs from which? State the reasons of your chosen test/method and interpret your conclusions.

2. Hypothesis testing and CI

Two groups of female rats were placed on diets with high and low protein contents and the gain in weight between $28^{\text {th }}$ and $84^{\text {th }}$ days of age was measured for each rat.

1. Weight gains for the two diets are normally distributed. What test would you use to see if weight gain differed between the two? Explain your reasons of chosen test.
2. If mean \((\mathrm{HP})=120\), mean \((\mathrm{LP})=101\) and and Standard Error (mean HP mean LP) \(=10.04\), calculate the value of the test statistic (z-test) using a calculator.
3. Calculate an estimate of the effect size together with \(95 \%\) confidence interval using calculator. 3 marks
   Now calculate the \(95 \%\) CI using SPSS (show the SPSS output). Do they differ from the CI you calculated using calculator? If so why?
4. The \(p\) value is 0.08. What would you interpret? 4 Marks
5. The researcher is disappointed with the large range of uncertainty. What could be done? 4 marks

3. Hypothesis testing and CI

The following table shows the results of a laboratory experiment in which mice are injected with two different types of vaccine thought to be protective against tumour development. The first vaccine contained MUC1 antigen only and the second contained MUC1 antigen + Caspases protein. The number of mice that developed a tumour after 62 days was recorded for each group.

1. Given these data and the total number of mice, which test should you use with this data to compare the effects of the two vaccines and why?
2. Find the expected values for all the cells [all calculations: 2 decimal places].
3. Use this test to examine whether the \(\mathrm{MUC1}\) + Caspases vaccine is more effective at protecting against tumour growth compared to the MUC1 only vaccine [all calculations: 2 decimal places].
4. What is the risk of an event (tumour) in each of the MUC1 and MUC1 + Caspases groups? Calculate the relative risk of a tumour growing for the \(\mathrm{MUC} 1+\) Caspases vaccine and interpret it.

Price: $26.99

Solution: The downloadable solution consists of 13 pages, 1399 words and 12 charts.
Deliverable: Word Document