4. Materials and Methods
4.5 Data Analysis Methods
The statistical significance of different measurements was tested with statistical tests using SPSS Statistics 22 -software (IBM, USA). Here the theories of the used tests are explained.
4.5.1 Normalization
ADC values of lesions were normalized with ADC value obtained from the reference point. Normalized ADC value ADCn were determined with following calculation:
reference lesion
n ADC
ADC = ADC , (16)
where ADClesion is the ADC value of actual lesion and ADCreference the mean ADC val-ue from reference ROI. The more consistent results with literature valval-ues (Table 1) were achieved by using the reference point from high intensity area.
4.5.2 Signal-to-noise ratio
Signal-to-noise ratio was determined from b=0 s/mm2 diffusion images according the NEMA Standards 1-2008. SNR was obtained by dividing the image signal by the image noise:
noise signal
SNR= , (17)
where signal is the mean signal measured from the lesion and noise is determined from the background of the image (outside of tissue area). The change of noise distribution must be modified because the SNR measure assumes the noise is Gaussian distributed.
In this work the noise was corrected as:
66 . 0
noise= SD , (18)
where SD is the standard deviation measured from the background and the factor of 0.66 (≅
(
4−π)
2) accounts for the Rayleigh distribution of the noise. The equation (17) was used to determine the SNR of the images. SNR was measured from 19 images and the final value was averaged from these.4.5.3 Statistical methods
Before making any conclusions of statistical research results, they are usually being tested. This is often made through a statistical hypothesis testing. First a null-hypothesis H0 is formed, which expresses the desired condition, e.g. “sample values are normally distributed”. Also an alternative hypothesis H1 is defined, which can be allowed if null-hypothesis is rejected, e.g. “sample values are not normally distributed”. Next the statis-tical test is chosen to prove which hypothesis is correct. In this context also a signifi-cance level α for significant and nonsignificant statistics is defined. Common values for significance level are 5% and 1%.
Not always the hypothesis is selected correctly after the statistical test. Thus, two kinds of errors may occur; rejecting the null-hypothesis Ho when it is true or accepting it when it is false. These two errors are called as Type I and Type II errors, respectively.
One way to avoid errors is to select appropriate significance level α. [49; 50]
Kolmogorov-Smirnov test
Kolmogorov-Smirnov test utilises cumulative distributions to compare experimental results with reference distributions [49]. In this work it was used to test if data samples were normally distributed. The null-hypothesis H0 was set as “The distribution of meas-ured values is Gaussian” and the alternative hypothesis H1 as “The distribution of measured values is not Gaussian”.
In Kolmogorov-Smirnov test the sample cumulative frequency sum Fn(x) is de-termined for the data. This is then compared with cumulative distribution function of the reference distribution Fe(x):
where D is the difference. If the difference D does not exceed the appointed significance level α, the null-hypothesis is accepted. [50] In this thesis Kolmogorov-Smirnov test was used to test the normal distribution of samples.
t test
The tests for a difference between two means can be divided into two cases: samples large enough that the sample standard deviations are not practically different from known and the case of small-sample estimated standard deviations. The mean test uses a
standard normal distribution (z distribution) in the first case and a t distribution in the second one, and the tests are called z test and t test, respectively. [50]
Before the actual t test, the normality of the sample is tested (e.g. with Kolmogo-rov-Smirnov test). Then the null- and alternative hypotheses are specified. The null hy-pothesis H0 is usually set as” the means are the same”, H0:µ1 =µ2. The alternative hy-pothesis H1 “the means are not the same” may be set as two-sided test, H1:µ1 ≠µ2 or as one-sided test, H1:µ1<µ2 or H1:µ1 >µ2. By choosing the significance level, the critical t value can be determined from statistics tables. For the sample, the t value is calculated as:
t µ1−sµ2
= , (20)
where s is determined through following equation:
where niis sample size and siis sample’s standard deviation. Finally the null hypothesis is either accepted or rejected, depending on where the statistics lies relative to the criti-cal value. [50] In this work t test was used to test if mean ADC values of benign and vary from 0 to 1 and the closer to unite they are, the more reliable the tested method is.
The repeated measurements were analysed with SPSS using the averages of intra-class correlation coefficients (ICCs) with absolute agreements.
Sensitivity and Specificity
Sensitivity tells the proportion of true positive cases, so the event of a predicted disease being present. Specificity instead, also called true negative, is the event of predicting no disease when disease is absent. [50] In this thesis these concepts were used alongside with the ADC threshold values; for example threshold ADC value for malign lesions X.
Sensitivity is determined with ratio:
6768898: ;<=>?@ AB C?DEAFD GEH IJK LMC<? D=MCC?@ HMF N
;<=>?@ AB =MCEOF C?DEAFD (22)
Respectively the specificity is described with ratio:
6PQ8R8Q8: ;<=>?@ AB >?FEOF C?DEAFD GEH IJK LMC<? O@?M?@ HMF N
;<=>?@ AB >?FEOF C?DEAFD (23) Sensitivity and specificity were used to evaluation the cutoff ADC value of malign le-sions.