Components of Statistical Analysis
The use of statistical analysis allows one to manage and analyze data in a way that allows drawing fact-based conclusions supported by evidence. Many human activity industries require the maintenance of superior accuracy, without which the outcomes of such activities can be fatal. For example, high accuracy is necessary in the pharmaceutical industry to manage drug dosages and avoid fatalities.
Another example would be the energy industry, especially those based on nuclear power. Miscalculations and mistakes in decision-making can be catastrophic not only for individual groups of people but for all of humanity. These are only two of the most prominent examples of such industries, where statistical procedures are vital tools for ensuring high accuracy and minimizing possible errors; in fact, there are many more. This essay discusses two components of statistical analysis that enable data-driven decision-making: confidence intervals and hypothesis testing.
Confidence Intervals
When conducting a statistical study, the researcher does not have access to data from the entire population for which the analysis is being conducted. For example, when a researcher wants to know the average score of all students taking a statistics course in the country, obviously limited resources make it impossible to know the scores for everyone in the population of interest. Instead, the researcher can turn to a small sample that proves to be representative enough to extrapolate its results to the entire population.
The ability to draw such a conclusion from sample data is motivated by the idea of confidence intervals. It is a tool that helps determine the boundaries of finding the number of interests with a certain degree of accuracy, usually with a 95% probability (Romer, 2020). In other words, by knowing the sample mean for student achievement, a researcher can calculate within what numerical bounds the population mean for that parameter lies.
Confidence intervals are an excellent solution for a situation in which one needs to find out the value of a parameter for a population based on sample data. However, there is a specific pattern that combines the limitations and advantages of this method. In particular, the apparent solution for a scientist may be to increase the accuracy of the final result — a desire that is not surprising since it is based on the need for a more accurate and reliable answer. Instead of boundaries defined by 95% probability, a researcher would rightly want to raise that level to 99% or even 99.9%.
However, increasing this accuracy has a downside: the higher the level of the confidence interval, the wider the boundaries for the parameter being determined. For example, for a sample of 100 respondents with a mean parameter value of 100 (SD = 10), the 95% confidence interval is defined in the range of 98 to 102, but the 99.9% interval is wider, with a range of 97 to 103. This widening is the price of increased accuracy because the wider the range, the more likely it is that the true value of the population parameter lies within it.
Hypothesis Testing
Another tool of statistical analysis is hypothesis testing. Hypotheses are statements that make assumptions about variables or the relationship between them. An example of such a hypothesis would be the belief that high student attendance leads to a higher final grade for the class. Hypotheses can be directional if the terms “more” or “less” are used for them or non-directional if equality is implied. However, hypotheses alone do not allow decisions to be made; they are only initial settings for analysis.
Depending on the type of data collected and the purpose of the study, various statistical tests can be applied for processing. These can include regression analysis, ANOVA, t-tests, Chi-Square tests, and other forms of data examination. Regardless of the test, it ultimately yields some results with a calculated level of significance called the p-value (Bevans, 2021). If this p-value is higher than the critical level of significance and recorded as alpha, then the null hypothesis must be accepted, and vice versa.
Thus, hypothesis testing is based on conducting a statistical analysis and seeking to compare the calculated p-value to the alpha. An example would be the null hypothesis that there is no relationship between the variables “Attendance” and “Final Score,” while the alternative hypothesis postulates the opposite: this is an example of a non-directional hypothesis. The data were quantitative, so a regression analysis to evaluate the nature of the relationship between them would be appropriate.
As a result, the significance of the regression model itself would have been calculated and would have had a specific value. If this value was higher than the significance level chosen earlier, such as.05, then the null hypothesis was accepted. If the value was lower, then the results would be accepted as statistically significant; that is, the relationship between the variables would be valid.
References
Bevans, R. (2021). Hypothesis testing | a step-by-step guide with easy examples. Scribbr. Web.
Romer, D. (2020). In praise of confidence intervals [PDF document]. Web.