The area of statistics is the art of discovering from data. It is a significant method used to investigate how we make explorations in science, make choices based on data, and make forecasts. Besides offering a deeper insights to the research topic and gain a better understanding of the overall concept, it helps you use the precise techniques to manage the data, employ accurate investigations, & efficiently display the events.
Today, data is everywhere. From journals, research articles to newspaper & internet, finding data is as easy as pie. Nevertheless, to collect reliable data, perform data analysis accurately or understand the underlying pattern of data, we require statistical tools & techniques to deep down within.
In this blog we will uncover the sophisticated statistical techniques which help you explore & summarize the data and represent their underlying patterns.
Mean, often regarded as arithmetic average, derives the central tendency of the data to be examined. In other words, it is the sum of all the records divided by the number of records. Mean helps the researcher to discover the overall trend of data by providing a speedy picture of the entire data. It also eliminates the random error and offers accurate data analysis outcome. Another added benefit of this measure is that it’s pretty simple and quick to measure. The mean can easily inaccurate in case of outliers and can show skewness in the data. The formula for the mean :
x = each observation
n = number of observations.
However, using mean alone can be proved dangerous for any prediction as it can be confused with the median or mode for some sample. Also, the mean may get affected by extreme variables or outliers in the data to be examined.
The standard deviation estimates the spread of data or average range around the mean. It is the square root of the variance and provides a knowledge of the ‘standard’ distance of the average. A high standard deviation implies that the data is widely spread from the mean. On the other hand, lower standard deviation signifies that data is aligned with mean. This type of statistical technique is used to determine the dispersion of data points and can be determined by
Estimating the deviation of each value of the mean
Squaring each value of the mean
Adding the squared deviations
Divide by the number of items -1.
The formula that is used to calculate standard deviation is:
X: sample mean
Xi : ith element
N: number of elements
An equation that provides the variance of standard deviation is:
Similar to mean, considering standard deviation all alone won’t provide you with the desired outcome. For instance, data with weird pattern such as non-normal curve is under the examination, then standard deviation won’t offer the detailed information of the data.
Sample Size Determination
Sample size determination plays a crucial role in statistical tests. If the sample size is not selected appropriately, then the conclusion drawn from the test may not reflect the actual scenario. Sample size can be determined based on the criteria of the degree of precision, degree of variability and by considering the desired confidence level. The formula employed to determine the sample size on the basis of confidence level is:
Where ‘n’ is the required sample, ‘p’ is the proportion of the population, ‘d’ is the degree of precision and q=1-p.
Identifying the right sample size is definitely a tricky process. The best option here is to collaborate proportion and standard deviation approaches and determine the accurate sample size.
However, the drawback is experienced when using proportion method. For example, while studying an untested variable, the proportion equations might rely on several assumptions which might not be accurate. This error will then be passed on the sample size and thereby to the data analysis.
Regression is a robust statistical approach which examines the relationship between dependent and independent variable. Here, the dependent variable needs to be defined in order to identify the impact of independent variable on the dependent. The added advantage of using regression is it specifies the strength of the variable under study. However, under certain circumstances, regression can be considered insignificant. For instance, the outlying data may represent the input from highest selling product. The regression line then ignores these outliers.
Commonly regarded as T-testing, hypothesis testing evaluates if a specific premise is true for given population or data set. In data analysis, the outcomes of the hypothesis is considered to be significant if the results of the analysis didn’t happen on random basis. However, while performing hypothesis testing one might face errors such as type I and type II errors which need to be taken into account.
To summarize, the above mentioned measures play a role in decision-making process in statistics. However, avoiding the pitfalls associated with each measure is important to ensure the accomplishment of data analysis.