Functions of Statistics
Firstly, statistics is used to present facts in a simplistic manner. This makes statements more convincing and logical as compared to mere description. Secondly, statistics is used to reduce complexities associated with raw data enabling the readers draw interpretations and inferences. There are various statistical measures that are used to make raw data simple and intelligible (LeBlanc, 2004). Examples are; graphs, dispersions, averages, regressions, correlation and kurtosis. Thirdly, statistics facilitates comparison. Comparisons are important when the user of a given data set draw conclusions between two groups or the past and present. Statistical devices such as ratios, averages and coefficients are used in making comparisons. Fourthly, hypothesis testing is another core function of statistics. Consequently, hypothesis testing is used to develop new theories. Examples of statistical devices used in hypothesis testing are t-test, regression analysis and chi-square. Fifthly, statistics is used to formulate policies and plans (LeBlanc, 2004). One of the initial phases of policy formulation is statistical data analysis. Therefore, the importance of statistics to scientists, economists, planners and administrators in preparation of programmes and plans cannot be overemphasised. Sixthly, statistics is used in forecasting. Statistics used past data to forecast trends and tendencies that will occur in the future (LeBlanc, 2004). For example planners can forecast future population basing on the current trends in population growth. Some of the statistical devices used in forecasting future trends are regression analysis and graph extrapolation. Lastly, statistics is used to derive inferences from an enquiry (LeBlanc, 2004). Often scientists and planners use the information obtained from a sample to draw inferences about the entire population.
Descriptive and Inferential Statistics
Descriptive statistics refers to statistical measures that are used in describing the population of interest (Peck & Devore, 2011). Descriptive statistics is used to summarize important information about data that was obtained from the population that is being studied (Peck & Devore, 2011). Descriptive statistics could in the form of a summary table or a chart/graph. Some of the statistical measures that are often included in the summary table are mean, median, mode, frequency, kurtosis, range, maximum value and minimum value. Examples of charts and graphs include a pie chart, bar graph and line graph. Charts and graph are often used to ensure that a person reading can understand the characteristics of a given population at a glance and give them a mental picture.
Inferential statistics refers to statistical measures that are drawing conclusions about the entire population from the analysis of a sample and observations. It takes analysis results of a sample and makes generalizations about the entire population from which the sample was taken. However, in order to make generalization, the sample must be a representative sample of the group (Healey, 2011). Inferential statistics is often done at a given level of significance. This is the probability that a wrong conclusion will be drawn from a given analysis (Healey, 2011). Significance level is often presented with the symbol α. The most prevalent level of significance is 5 per cent and 10 per cent.
Relationship between Descriptive and Inferential Statistics
It is noteworthy that the descriptive statistics and inferential statistics are often intertwined. This is because some inferential statistics uses some descriptive measures in drawing conclusions about the entire population. For example, t-test is used to make generalization about the population mean using the mean obtained from a sample. The sample mean in itself is a descriptive statistic. However, the mean is used in the t-test in estimating the population mean which is an inferential statistic.
Healey, J. F. (2011). Statistics: A Tool for Social Research (9 ed.). London: Cengage Learning.
LeBlanc, D. C. (2004). Statistics: Concepts and Applications for Science (illustrated ed.). New York: Jones & Bartlett Learning.
Peck, R., & Devore, J. L. (2011). Statistics: The Exploration and Analysis of Data (7 ed.). New York: Cengage Learning.