Question

Here are SPSS file no 1

survival time

43
45
53
56
56
57
58
66
67
73
74
79
80
80
81
81
81
82
83
83
84
88
89
91
91
92
92
97
99
99
100
100
101
102
102
102
103
104
107
108
109
113
114
118
121
123
126
128
137
138
139
144
145
147
156
162
174
178
179
184
191
198
211
214
243
249
329
380
403
511
522
598

2nd SPSS FILE

SURVIVAL TIME

49
98
44
72
215
41
65
80
58
60
57
142
115
93
73
79
120
80
101
82
81
137
57
63
123
102
81
222
90
93
238
126
110
99
87
115
144
162
127
152
145
91
179
82
255
185
145
83
191
199
175
220
83
91
79
87
107
74
94
66
117
116
106
108
87
237
97
163
54
114
131
60
73
136
115
145
118
91
92
155
95
175
139
101
125
161
103
117
270
125
113
241
159
97
283
133
217
196
143
97
201
160
188
105
99
107
206
237

3rd SPSS FILE

DOSE

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2

I uploaded all three SPSS files which are associated with these questions, the questions are

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?

Answer 1

The soultions are as explained below

Ln Tranformed data normally ditributes as

mean=Median=Mode

Dose 1 7 Dose 2 comparision

T-test for Mean survival rate

Ho:-

Ha=

Since P>.05 so we fail to reject H0.

So the mean survival rate for both Dose 1 & Dose 2 are not statistically different.

Yes, it conforms...

End of Answer!!