TFV0103 Tölfræði og fræðileg vinnubrögð
TFV0103 Tölvutími 5
Dæmi 1 (t-próf, Excel)
Sheepskin Mattress Experiment/Tilraun
In a long stay hospital ward, over a three-month period, ten patients laid on a mattress
covered with a normal sheet (Control/Samanburðarhópur), while another ten hospital
patients laid on a sheepskin covered mattress (Intervention/Inngrip). At the end of the threemonth period, the number of pressure sores (legusár) for each patient was observed as
follows:
Control
10, 8, 12, 13, 11, 10, 15, 7, 11, 10
Intervention 6, 4, 8, 7, 5, 6, 5, 10, 7, 5
Calculate the results of an independent t-test/óháð t-próf. (2-tailed test/tvíhliða próf, assume
unequal variances)
What significant level (marktektarstig) is reached?
What is the size of the effect (stærð áhrifa)?
Dæmi 2 (chi-squared test, Excel)
Chi-square test/kí-kvaðrat próf. Data in the form of cross-tabulation or contingency
tables/krosstöflur eða tenglsatöflur can be analyzed using the chi-square test. Consider the
following table showing the number of smokers/reykingamenn and non-smokers/menn sem
reykja ekki who either have or do not have cancer/krabbamein. The formula for chi-square is
shown below the table.
Observed/Fengitíðni Smokers
Cancer
230
No cancer
465
Non-smokers
78
652
(O - E) 2
  
E
all cells
2
In the formula, O stands for the observed frequency/fengitíðni in the cell/reitur and E stands
for the expected frequency/væntitíðni in the cell. To calculate E, you first calculate the row,
column and grand totals.
Observed/Fengitíðni Smokers
Cancer
230
No cancer
465
695
1
Non-smokers
78
652
730
308
1117
1425
TFV0103 Tölfræði og fræðileg vinnubrögð
The expected frequency/væntitíðni E in a cell is given by (row total x column total/grand
total). The expected frequencies are:
Expected
Cancer
No cancer
Smokers
150,2175
544,7825
Non-smokers
157,7825
572,2175
Enter the observed and expected data into Excel. In Excel, in a separate part of the
spreadsheet, calculate (O-E)2/E for each cell. You should obtain:
42,37348145 40,34187617
11,68400384 11,12381187
In Excel check that the value of chi-square when you add these numbers together is
105,5231733.
The degrees of freedom/frígráður is given by (R-1)x(C-1) where R is the number of rows and
C is the number of columns. Here the degrees of freedom is 1. With a degree of freedom
equal to 1, chi-square has to be bigger than 6,63 to obtain a p value of 0,01 or has to be
greater than 10,83 to obtain a p value of 0,001.
The null hypothesis/núlltilgatan that the independent variable/óháð breyta (smoking/nonsmoking) has no effect on the dependent variable/háð breyta (cancer/no cancer) is rejected
at the 0,001 level. We can conclude that smoking has an effect.
In Excel you can get the exact probability of obtaining the value of chi-square or greater by
using the CHITEST function. You can use the value of probability and the degrees of
freedom involved to obtain the actual value of chi-square by using the CHIINV function.
Chi-square critical values calculator
http://www.stat.sc.edu/~west/applets/chisqdemo.html
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