Explain and Execute Statistical Design and Analysis of Two Variable Hypothesis - Statswork

In this blog, I will explain to you how the statistical analysis is being applied for two independent samples. In practice, the test statistic used for comparing the two means from a population is by using the t-test because t-test shrinks the data to a single t-value and it is then compared with the significant value for the final conclusion. Now, let us understand the theoretical background in performing the t-test for two variables.

Suppose X1 and X2 be the two independent random variables and let, be the sample with size n1 and n2 from a population with mean µ1, µ2 and variance σ12, σ22 respectively.

Understanding the Problem Statement


The primary or basic task in any statistical data analysis is to know or find out what the problem is and how the data is being measured.

Construction of Test Hypotheses


Once you understand the problem at hand, the next step is to frame an appropriate hypothesis to test for statistical significance; we call it as the null hypothesis and alternative hypothesis (Flandin & Friston, 2019).

Finding a Suitable Test Statistics


For finding the suitable statistic test, we need to find the distribution of the data. I will illustrate with simulated data for two campaigns using R software.

Calculation of test statistic


Once you got all the necessary values for the calculation, the next step is to apply it to the formula of statistics test as mentioned earlier. Here, I will illustrate using R.

Conclusion of the Problem


As a final step, we compare the calculated t.value with the critical value. In order to find the critical value, we need to fix the significance level alpha. Usually, it is considered as 5% that means we can tolerate the probability of rejecting the null hypothesis by 5% or 0.05 level of significance. The next step is to check whether the null hypothesis is one-sided or two-sided for concluding the problem. If you are concerned about which campaign is higher or smaller then the null will be one-sided. However, in our case, it is a two-sided null hypothesis stating that the means of the campaigns are equal. An important note is that in a two-sided test the critical region is divided by half (5% is equally distributed in both sides from population mean).

References

Cressie, N. A. C., & Whitford, H. J. (1986). How to use the two-sample t‐test. Biometrical Journal, 28(2), 131–148. Retrieved from https://onlinelibrary.wiley.com/doi/abs/10.1002/bimj.4710280202

Flandin, G., & Friston, K. J. (2019). Analysis of family‐wise error rates in statistical parametric mapping using random field theory. Human Brain Mapping, 40(7), 2052–2054. Retrieved from https://onlinelibrary.wiley.com/doi/abs/10.1002/hbm.23839

Comments

Post a Comment

Popular posts from this blog

Foundations Of Public Policy Research And Primary Data Collection Methods — Statswork

Image
Public policies can be defined as the decision taken by the government in order to achieve certain goals and objectives formulated for the welfare of its people. Implementing and formulating the policies decided are based on a properly oriented pattern. In other words, the associated government agencies should be able to observe a well-defined relation between the policies implemented and formulated in order to decide the course of their activities (Peters, 2015). The following points further emphasize the meaning and characteristics of public policy. 1. Goal-oriented: The public  policies  defined by different organizations are formulated on the basis of a certain goal or are planned to keep in mind a particular goal which will be beneficial for the people of the country. These policies illustrate the different programs of the government and its concern towards different segments (Pierce, Peterson, & Hicks, 2017). 2. Public policies also reflect the decisions and th...
Read more

Driving Innovation: Leveraging Focus Groups for Strategic Decision-Making

Image
  Focus groups are pivotal in qualitative research, offering a dynamic platform for gathering in-depth insights from selected participants on specific topics. This method involves interactive discussions facilitated by a skilled moderator, allowing participants to share their opinions, experiences, and perceptions openly. Unlike individual interviews or surveys, focus groups capitalize on group dynamics, enabling participants to build upon each other's ideas and explore diverse viewpoints collaboratively. Advantages of Face-to-Face Data Collection 1. Enhanced Depth : Face-to-face interactions foster a conducive environment for deep exploration of topics. Participants can articulate their thoughts more freely, providing comprehensive insights that may be nuanced or multifaceted. 2. Non-verbal Cues : Beyond verbal responses, face-to-face settings capture non-verbal cues such as body language and facial expressions. These cues offer additional context to responses, enriching the unde...
Read more

Unveiling the Future: Advanced Analytics Tools Redefining 2024

Image
  Introduction: Why do we need advanced data analytics tools? Did you know that each human being on Earth generates approximately 1.8 MB of data every second? [1] With data increasing at a faster pace every day, it’s no wonder that some experts predict a data apocalypse is on the horizon. Data is an essential unit of construction for any organization, serving as a driving force for growth and success. However, as data grows, it’s becoming harder to manage and work using traditional database management systems. That’s where advanced data analytics tools come in. Big data analytics can help organizations handle large amounts of data more efficiently, providing acuities that can help drive decision-making. As data continues to be treated as an asset, it’s essential to stay up to date on the latest trends in data analytics tools. In this blog, we’ll investigate some of the latest trends in data analytics tools for 2024. Revolutionizing Industries: The Advantage of Advanced Analytics t...
Read more