Question

These are the questions and all three SPSS files which i uploaded are associated with these questions

tubercle bacteria

In an article to the Norwegian epidemiologist Tor Bjerkedal (1960): "Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli", American Journal of Hygiene, 72, 130-148, the survival time for guinea pigs injected with tuberculosis bacteria. Data is provided in the data file tubercle_bacilli.sav.

Provide a descriptive description of the data, with mean, median, standard deviation and any other descriptive targets that can describe this data.
Provide a 95% confidence interval for average, assuming normality.
Are the data normally distributed?
Transforms data using logarithmic transformation (using the function ln in SPSS). Are the data more normal in this case? Describe possible deviations from the normal distribution.
Provide a 95% confidence interval for the average of the logarithm to the survival time using the assumption that the logarithmically transformed data is normally distributed. What is the confidence interval if you are transforming back?
In the study of guinea pigs injected with tuberculosis bacteria, different doses of the amount of tuberculosis bacteria were tested. Data for two different doses are given in tubercle_bacilli_dose.sav. Dose 1 was a large dose of bacteria and dose 2 was a small dose of bacteria.
Write a numerical summary of survival times for guinea pigs for those who received dose 1 and for those who received dose 2.
Is the survival time of guinea pigs for dose 1 and dose 2 normalized?
What happens if you log-transform survival times? Will the data be more normalized?
Provide a 95% confidence interval for the average of the log-transformed survival times for those who received dose 1 and those who received dose 2, assuming that the log-transformed data is normally distributed. How is the confidence interval for dose 1 compared to the confidence interval for dose 2?
Is there a significant difference in the survival time of guinea pig who received dose 1 and dose 2? How does the dose depend on the level of bacteria along with the survival time?
An investigator of you will forget to check for the survival times of the guinea pigs for dose 1 and dose 2 is normally distributed before performing the two-sample t-test to check if there is a significant difference in the survival time of the guinea pigs. Perform the test. What conclusion does he come to? Does this conclusion differ from the one you found in point 10?

The referred data is

Here are SPSS file no 1

survival time

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598

2nd SPSS FILE

SURVIVAL TIME

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3rd SPSS FILE

DOSE

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Answer 1

Hi, We will be using SPSS in this problem:

Descriptive statistics for survival time:

Descriptive Statistics
	N	Range	Minimum	Maximum	Mean		Std. Deviation	Variance	Skewness
	Statistic	Statistic	Statistic	Statistic	Statistic	Std. Error	Statistic	Statistic	Statistic	Std. Error
Survival Time	180	557.0	41.0	598.0	131.583	6.0345	80.9618	6554.814	2.834	.181
Valid N (listwise)	180

Normal Q-Q plot:

Clearly, the data is not close to normal as the deviation is huge!

We shall transform the data into log transformation:

The normal Q-Q plot of the data is

We can see that data is closer to normal in case of log transformation.

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
Log_Survival	Equal variances assumed	3.221	.074	.459	178	.647	.03368	.07342	-.11121	.17857
	Equal variances not assumed			.434	123.697	.665	.03368	.07754	-.11979	.18715

As we can see that p-value is 0.07 so at level of 5%, we can NOT reject the NULL.