Please read below discussion posts and respond utilizing your own words.

A) Your definition of correlation made it very clear that it is different between causation and put an emphasis on how two variables would be identified as correlation. The way that you described correlation allowed me to think a lot about how different statistics could be correlated but not related at all. Although I understood that correlation does not equal causation, I appreciate how your response included different examples of how correlation and causation are not related. The various examples under each allowed me to really recognize all the ways that we may think variables can be causation when they really are not! The most interesting to me is the confounding factors because there is usually another factor that can describe the relationship that is being examined.

B) Correlation does not equal causation primarily because correlation measures only the strength and direction of a linear relationship between two variables, but it does not indicate whether one variable causes changes in the other (Smith, 2018). Two variables may exhibit a strong correlation due to a variety of factors, including the presence of a third variable that influences both, or mere coincidence. For instance, the number of ice creams sold in a city might strongly correlate with the number of drowning incidents, but this does not imply that buying ice cream causes drowning. Both variables are likely influenced by a third factor: hot weather. This phenomenon is known as the "third-variable problem" or "confounding variable" (Smith, 2018). Correlation does not account for the temporal sequence required to establish causation. For causation to be confirmed, the cause must precede the effect in time (Zyphur & Osald, 2015). A high correlation might exist between two variables, but without establishing that one variable changes before the other, we can't infer a causal relationship. Experiments and longitudinal studies, which observe changes over time, are necessary to disentangle such relationships and potentially establish causation. Thus, while correlation can suggest a possible relationship worth investigating, it is not sufficient evidence to conclude that one variable causes changes in another (Zyphur & Oswald, 2015).

C) The correlational design is a research method used to explore the relationship between two variables without manipulating or controlling them (Corty, 2016). It aims to understand the connection between the variables without assuming a cause-and-effect relationship. While correlations and causations may seem related, they are distinct statistical concepts (Anderson & Geras, 2022). Correlation indicates a relationship or pattern between two variables, while causation suggests that one event directly influences another. For example, not getting enough sleep causes drowsiness. It is crucial to understand that when there is a correlation between variables, it does not necessarily mean that one variable causes the other. The observed association may be coincidentally or occur by chance (Chen & Utter, 2021). Reverse causality refers to events A and B that are causally related but not in the expected order. This could occur when a third confounding variable influences both events. In some cases, an underlying variable might cause the events to appear correlated, leading us to mistakenly believe that event A causes event B when another event, C, is responsible for events A and B. Understanding correlation can be straightforward because it is easy to observe, but establishing causation is far more complex and demands a well-designed experimental approach (Chen & Utter, 2021).

D) Correlation is a useful statistic when looking at a relationship between two variables. With correlation statistics, the two variables happen naturally and are not manipulated in any way and their results are studied to see their relationship (Corty, 2016). It is considered common because correlation can help us recognize in public health how behaviors and diseases interact, how prevention/medications interact, and how disparities can affect health. The biggest takeaway for correlation statistics is that the variables are observed just the way they are in life, there is no room for manipulation of the variables. The natural relationship between the two variables helps continue the study of the subjects. This is because the information we are trying to find does not relate to cause and effect or the causes of the two variables (Corty, 2016). This is where we stress that 'correlation does not equal causation.' There can be many variables that cause another, selecting one alone without enough evidence is not being the diligent researcher that is needed in public health. We can see a strong relationship between two variables, but that does not mean they are related in the sense of cause and effect. So many unrelated things, like an increase in tennis shoes and an increase in heart conditions, can have an association, but that does not mean that they are related.

E) In statistics, parametric and nonparametric tests are two important types of statistical tests to analyze data. According to Corty, parametric tests are statistical tests that are designed to be used with interval or ratio-level outcome variables which require that specific assumptions about the underlying population are met (2016). These tests are really useful and provide researchers with precise estimates when the assumptions are met. The most common parametric statistical test that is used is the t-test (Kim, 2015). Parametric tests are also best used for larger samples.

Nonparametric are much more different than parametric tests. Corty defines nonparametric tests as a statistical test that are suitable for nominal ordinal-level outcome variables that do not require assumptions about the population distribution (2016). These types of tests are very versatile and they can be applied to ordinal data or data that isn't really distributed normally. The two most common nonparametric statistical tests are the chi-squared good-of-fit test and the chi-square test of independence (Corty, 2016). To determine whether to use parametric or nonparametric tests for analyzing data, there are factors to consider. If the researcher wants accurate results specifically using nominal or ordinal data, nonparametric tests would be the best to use (Corty, 2016). On the other hand, if there is interval/ratio level data, parametric tests would be best. In summary, the decision between whether to use parametric or non-parametric tests depends on the characteristics of the data and the type of data that is being recorded.

F) Parametric tests are tests that make assumptions about the parameters of the population distribution from which a sample is pooled. here are five assumptions from a parametric test, they are normality, independence, homogeneity, randomness, absence of outliers, and linearity (Klintberg et al., 2022). An example of a parametric test is anANOVA test (Analysis of variance). It is a statistical test used to analyze the difference between the means of two groups, a one-way ANOVA uses one independent variable while a two-way ANOVA uses two independent variables.

Non-parametric tests are studies or experimentsthat do not require the underlying population for assumptions. It does not rely on data referring to any particular group of probability distributions (Ohunakin et al., 2024). They are also called or referred to as distribution-free tests. An example of a non-parametric test is the Chi-Squared test, it is a statistical test used to check if two categorical variables are related or independent. It compares two datasets that can be used to conclude the associations between variables.

The difference between the two is that a parametric test makes assumptions about a population's parameters, and a non-parametric test does not assume anything about the underlying distribution.

Parametric tests are suitable for normally distributed data whereas non-parametric tests are suitable for any continuous data, based on ranks of the data values.