How to Read and Independent Sample T Test
Independent samples t-test
Description
The contained samples (or two-sample) t-examination is used to compare the means of two contained samples.
Required input
Select the variables for sample one and sample ii. Differences will be calculated every bit Sample2−Sample1.
Caveat: the two filters must ascertain distinct groups then that the same case is not included in the two samples.
Options
- Logarithmic transformation: if the data require a logarithmic transformation (e.g. when the data are positively skewed), select the Logarithmic transformation pick.
- Confidence interval: select the required confidence interval for the difference between the means. A 95% conviction interval is the usual choice, select a xc% confidence interval for equivalence testing.
- Correction for unequal variances: allows to select the t-test (bold equal variances) or the t-test corrected for diff variances (Welch test, Armitage et al., 2002). With the option "Automatic" the software will select the advisable examination based on the F-examination (comparison of variances).
- Residuals: optionally, select a Test for Normal distribution of the residuals. In the independent samples t-test, residuals are the differences between the observations and their group or sample mean.
Results
The results windows for the Contained samples t-test displays the summary statistics of the ii samples, followed by the statistical tests.
First an F-test is performed. If the P-value is low (P<0.05) the variances of the two samples cannot be causeless to be equal and it should exist considered to use the t-test with a correction for unequal variances (Welch examination) (see above).
The independent samples t-examination is used to test the hypothesis that the difference betwixt the means of 2 samples is equal to 0 (this hypothesis is therefore called the zip hypothesis). The program displays the departure between the two means, and the confidence interval (CI) of this difference. Next follow the examination statistic t, the Degrees of Freedom (DF) and the two-tailed probability P. When the P-value is less than the conventional 0.05, the null hypothesis is rejected and the conclusion is that the ii ways do indeed differ significantly.
Logarithmic transformation
If you selected the Logarithmic transformation selection, the program performs the calculations on the logarithms of the observations, but reports the back-transformed summary statistics.
For the t-examination, the difference and its confidence interval are given, and the test is performed on the log-transformed scale.
Next, the results of the t-examination are transformed back and the interpretation is every bit follows: the back-transformed divergence of the means of the logs is the ratio of the geometric ways of the 2 samples (come across Banal, 2000).
Normal distribution of residuals
For the independent samples t-test, it is assumed that the residuals (the differences betwixt the observations and their grouping or sample mean) follow a Normal distribution. This assumption tin can exist evaluated with a formal examination, or by means of graphical methods.
The different formal Tests for Normal distribution may not accept enough ability to discover departure from the Normal distribution when sample size is small. On the other hand, when sample size is big, the requirement of a Normal distribution is less stringent considering of the central limit theorem.
Therefore, it is often preferred to visually evaluate the symmetry and peakedness of the distribution of the residuals using the Histogram, Box-and-whisker plot, or Normal plot.
To practise so, you click the hyperlink "Relieve residuals" in the results window. This volition save the balance values as a new variable in the spreadsheet. You can and then use this new variable in the unlike distribution plots.
One-sided or two-sided tests
In MedCalc, P-values are ever ii-sided (as recommended past Fleiss, 1981, and Altman, 1991) and not one-sided.
A two-sided (or ii-tailed) P-value is appropriate when the difference between the two means tin occur in both directions: it may exist either negative or positive, the mean of i sample may either be smaller or larger than that of the other sample.
A one-sided test should only be performed when, earlier the get-go of the study, it has already been established that a divergence can only occur in one direction. E.m. when the mean of sample A must be more than the hateful of sample B for reasons other than those connected with the sample(s).
Interpretation of P-values
P-values should non be interpreted too strictly. Although a significance level of 5% is by and large accustomed every bit a cutting-off point for a pregnant versus a not-meaning event, it would exist a mistake to interpret a shift of P-value from e.grand. 0.045 to 0.055 as a modify from significance to non-significance. Therefore the real P-values are preferably reported, P=0.045 or P=0.055, instead of P<0.05 or P>0.05, so the reader can make his own estimation.
With regards to the estimation of P-values equally significant versus not-meaning, is has been recommended to select a smaller significance level of for example 0.01 when it is necessary to be quite certain that a difference exists before accepting it. When a study is designed to uncover a difference, or when a life-saving drug is being studied, nosotros should be willing to accept that in that location is a divergence even when the P-value is every bit big every bit 0.x or even 0.twenty (Lentner, 1982). The latter authors state that "The trend in medical and biological investigations is to use also small a significance probability".
Confidence intervals
Whereas the P-value may give information on the statistical significance of the consequence, the 95% conviction interval gives information to assess the clinical importance of the effect.
When the number of cases included in the written report is large, a biologically unimportant difference tin can be statistically highly pregnant. A statistically significant result does not necessarily indicate a real biological difference.
On the other paw, a loftier P-value can lead to the decision of statistically non-significant divergence although the divergence is clinically meaningful and relevant, especially when the number of cases is pocket-size. A non-significant issue does not mean that at that place is no real biological departure.
Confidence intervals are therefore helpful in interpretation of a deviation, whether or not it is statistically significant (Altman et al., 1983).
Presentation of results
It is recommended to written report the results of the t-examination (and other tests) not past a simple statement such as P<0.05, simply by giving full statistical data, equally in the following example by Gardner & Altman (1986):
The difference between the sample hateful systolic claret force per unit area in diabetics and non-diabetics was 6.0 mm Hg, with a 95% confidence interval from one.1 to 10.9 mm Hg; the t exam statistic was 2.4, with 198 degrees of freedom and an associated P value of P=0.02.
In short:
Mean 6.0 mm Hg, 95% CI 1.1 to ten.9; t=2.4, df=198, P=0.02
Literature
- Altman DG, Gore SM, Gardner MJ, Pocock SJ (1983) Statistical guidelines for contributors to medical journals. British Medical Periodical, 286, 1489-1493.
- Armitage P, Drupe Thousand, Matthews JNS (2002) Statistical methods in medical research. 4th ed. Blackwell Science.
- Banal Grand (2000) An introduction to medical statistics, 3rd ed. Oxford: Oxford University Press.
- Fleiss JL (1981) Statistical methods for rates and proportions, 2nd ed. New York: John Wiley & Sons.
- Gardner MJ, Altman DG (1986) Confidence intervals rather than P values: estimation rather than hypothesis testing. British Medical Journal, 292, 746-750.
- Lentner C (ed) (1982) Geigy Scientific Tables, 8thursday edition, Volume ii. Basle: Ciba-Geigy Limited.
See also
External links
How to Read and Independent Sample T Test
Source: https://www.medcalc.org/manual/ttest.php
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