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Independent t tests and χ tests for independence were used to compare groups on continuous and categorical data respectively.
Descriptive statistics were presented by nonfrail and frail patients, and differences between groups were assessed via Mann–Whitney U test or Student's t-test for independent samples and Pearson's chi-square tests or Fisher's exact tests for independence.
To test the hypothesis that frequencies of observed live, necrotic, and apoptotic cells were independent of the staining method used, we employed chi-square tests for independence in contingency tables using Microsoft Excel.
Hypothesis tests and confidence intervals for population variances, chi-squared goodness-of-fit tests, hypothesis tests for independence, simple linear regression model, testing regression parameters, prediction, multiple regression, omitted variable bias, multicollinearity, F-tests, regression with indicator random variables, simultaneous equation models and instrumental variables.
Tests for independence of dependent variables and response were performed using chi-square tests for independence.
To determine if proportions were different between 2006 and 2010, chi-square tests for independence were used.
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Within subjects correlation, chi-squared test for independence, and independent samples t-test were used to analyse the data.
Differences between groups were analysed using independent sample t-test and chi-square test for independence.
Testing for independence between two covariance stationary time series, Biometrika 83 (1996), 615-625.
To test for independence (spatial correlation), we plotted the standardized residuals against their spatial co-ordinates17.
Cocoa plantations were assigned to a five-class typology and tested for independence with growing region using contingency analysis.
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