Help with choosing the right method

#1
Hi

I'm new to stats as you will probably become aware.

Just need a little help to understand which statistical method should be
used to test a hypothesis.

The work centres around a surgical endoscopy procedure for the taking of biopsy samples. The hypothesis states that with an increase in the number of procedures carried out there should be a lowering in the time the procedure takes and the number of attempts to take a clean biopsy.

!2 procedures have been observed and the data collected as follows.

Procedure Time Taken Attempts
1 90min 3
2 80min 2
3 90min 3
4 60min 2
5 60min 2
6 60min 2
7 90min 3
8 60min 2
9 60min 3
10 60min 4
11 30min 2
12 20min 2
Mean 63.3 2.5
Mode 60 2
Median 60 2
S.Deviation 19.79 0.622

Any advice on the method I should use to prove/disprove the hypothesis would be appreciated.

I was suggested to use a chi-square calculation which I did and got the following: Df=11 Chi-square=4.3140201607494 with the significance level at .05, chi-square should be 19.68 and therefore the distribution is not significant. p <= 1.

I don't know if this was the right test or if it is the start of another but any help would be appreciated.

Kind regards
Andrew
 

JohnM

TS Contributor
#2
I would do two regressions, with Procedure as the x or independent variable, and Time Taken and Attempts as the y or dependent variables.

If Time and Attempts are in fact decreasing, the regression lines should slope downward as Procedure "increases." Additionally, test to see if r > 0 and if the slope of the line is > 0.
 
#3
Hi

Ok I did the linear regression and got these results butI am confused as to there meaning.

slope m= -5.673758865
y-int, b= 100.212766
r= -0.911211378

Andrew
 

JohnM

TS Contributor
#7
slope m= -5.673758865
The slope represents the change in y for each unit change in x. In this case, it means that for each successive procedure, the time should be reduced, on average, by about 5.7 minutes.


y-int, b= 100.212766
The y-intercept is where the regression line will cross the y-axis, in other words, how long would a procedure take if x=0. However, in your case, the lowest meaningful x value is 1, so you may want to estimate where the regression line intersects the vertical line x=1. That would give you the estimated time, on average, that it takes to complete the procedure on the very first attempt.

r= -0.911211378
r is the strength of the linear relationship between x and y, and can range from -1.0 to +1.0. A value of -0.91 indicates a strong negative relationship - i.e., as x increases, y tends to decrease (as the number of procedures increases, the time taken to complete them tends to decrease).
 
#8
Great thanks for all the help John.

I've even attempted a chi-squared test with a significant result which I've attached below.

Is this helpful for this exercise

Andrew