In recent years, information about a person can be extracted just from the person's voice signals using certain computational systems. Additionally, it can then be determined whether a person is affected or not by a severe medical condition like Parkinson's Disease (PD). This shows that there is a certain distinct connection between PD and speech impairment. Moreover, it is known that early detection of the disease can result in a better medical diagnosis and treatment. In this research paper, a versatile range of classification based machine learning and deep learning algorithms, employed with different dimensionality reduction (DR) techniques are used. A comparative study of their accuracies in differentiating a healthy human from one who is afflicted by the disease is performed. The time complexities of the algorithms have also been observed to understand the effect of DR techniques. These algorithms have been trained on the Parkinson's speech dataset obtained from UCI machine learning repository. © 2018 IEEE.