In recent studies, in the field of Brain-Computer Interface (BCI), researchers have focused on Motor Imagery tasks. Motor Imagery-based electroencephalogram (EEG) signals provide the interaction and communication between the paralyzed patients and the outside world for moving and controlling external devices such as wheelchair and moving cursors. However, current approaches in the Motor Imagery-BCI system design require effective feature extraction methods and classification algorithms to acquire discriminative features from EEG signals due to the non-linear and non-stationary structure of EEG signals. This study investigates the effect of statistical significance-based feature selection on binary and multi-class Motor Imagery EEG signal classifications. In the feature extraction process performed 24 different time-domain features, 15 different frequency-domain features which are energy, variance, and entropy of Fourier transform within five EEG frequency subbands, 15 different time-frequency domain features which are energy, variance, and entropy of Wavelet transform based on five EEG frequency subbands, and 4 different Poincare plot-based non-linear parameters are extracted from each EEG channel. A total of 1,364 Motor Imagery EEG features are supplied from 22 channel EEG signals for each input EEG data. In the statistical significance-based feature selection process, the best one among all possible combinations of these features is tried to be determined using the independent t-test and one-way analysis of variance (ANOVA) test on binary and multi-class Motor Imagery EEG signal classifications, respectively. The whole extracted feature set and the feature set that contain statistically significant features only are classified in this study. We implemented 6 and 7 different classifiers in multi-class and binary (two-class) classification tasks, respectively. The classification process is evaluated using the five-fold cross-validation method, and each classification algorithm is tested 10 times. These repeated tests provide to check the repeatability of the results. The maximum of 61.86 and 47.36% for the two-class and four-class scenarios, respectively, are obtained with Ensemble Subspace Discriminant among all these classifiers using selected features including only statistically significant features. The results reveal that the introduced statistical significance-based feature selection approach improves the classifier performances by achieving higher classifier performances with fewer relevant components in Motor Imagery task classification. In conclusion, the main contribution of the presented study is two-fold evaluation of non-linear parameters as an alternative to the commonly used features and the prediction of multiple Motor Imagery tasks using statistically significant features.