SYSE 515 4.3 Statistics in Action

 The past 2 modules were full of essential factors that are necessary in statistics.

I would like to take my blog post today as an opportunity to review some of these essential factors.

Bernoulli trial

The Bernoulli trial is also called the binomial distribution function and it is used to analyse discrete random variables.

The basic assumptions of the Bernoulli trial are that:

(1) each trial has only two outcomes, either occurrecne or nonoccurrence.

(2) the probability of occurrence of any one trial is p, which is the same for all trials.

(3) the trials are statistically independent.

One of the easy examples is flipping coins. For the example, since the success rate and non success rate are 0.5 and it meets all the conditions that is listed above, the Bernoulli trial can be applied here.

However, in a case where there are human drug trials, some may assume that Bernoulli trials can be applied because on the surface it sounds like a binary problem with success or failure as the two outcomes. While the case complies to conditions (1) and (3), patients might have all different medical backgrounds and represent different demographics which may affect probability of the test success or failure rate. In this case, only if the patients somehow had exactly the same medical background and demographics, could the Bernoulli trial be applied.

Central Limit Theorem

It is an easy concept to understand, yet it is important. If the mean of population is μ and the variance is σ², and if the sample size is big enough (usually n≥30), then the sample's mean S bar should look like it follows normal distribution.

To standardize the theorem,

Z= Z-score of the observations

µ= mean of the observations

α= standard deviation

n= sample size

With that, the standard normal distribtution table can help to find more data with the given inputs in problems.

Statistical hypothesis testing

Appropriate hypothesis testing needs to be done to be able to effectively predict the results for the whole population by testing samples.

Hypothesis have two parts which are the null hypothesis (H₀₎ and the alternative hypothesis ₍H_1).

If a null hypothesis is rejected, an alternative hypothesis hypothesis is accepted and vice versa.

The null hypothesis is rejected if the test statistic value is outside the critical value.

Like other statistical methods, hypothesis testing has its limitations. Even if the null hypothesis isn't rerjected based on the test result, it doesn't mean a null hypothesis is true. A rejected null hypothesis indicates the samples used to assume the population could have completely different results depending on the sampling process.

One-way Analysis of Variance (ANOVA)

If there are three or more than three groups that require analysis on their differences, an ANOVA test can be done by testing the means of the groups. A one-way ANOVA is done if there are two or more independent variables. While a one-way ANOVA test tells if there are any differences between the variables, it doesn't provide accurate data on which variables are different.

References:

Rose, A. (2018, March 5). Base. Alex’s Machine-Learning. https://lee-soohyun.tistory.com/82

Central Limit Theorem. (n.d.). WallStreetMojo. Retrieved September 6, 2020, from https://www.wallstreetmojo.com/central-limit-theorem/

Singh, S. (2018, May 23). Central Limit Theorem Simplified! - Seema Singh. Medium. https://medium.com/@seema.singh/central-limit-theorem-simplified-46ddefeb13f3

Taylor, C. (2019, June 24). Differences Between The Null and Alternative Hypothesis. ThoughtCo. https://www.thoughtco.com/null-hypothesis-vs-alternative-hypothesis-3126413