Pearson Correlation Research Question Example

[Florencia Abila]

Ingeneral, a researcher should use the hypothesis test for the population correlation \(\rho\) to learn of a linear association between two variables, when it isn't obvious which variable should be regarded as the response. Let's clarify this point with examples of two different research questions.

By contrast, suppose we want to evaluate whether or not a linear relationship exists between a husband's age and his wife's age (Husband and Wife data). In this case, one could treat the husband's age as the response:

To obtain the P-value, we need to compare the test statistic to a t-distribution with 168 degrees of freedom (since 170 - 2 = 168). In particular, we need to find the probability that we'd observe a test statistic more extreme than 35.39, and then, since we're conducting a two-sided test, multiply the probability by 2. Minitab helps us out here:

The output tells us that the probability of getting a test-statistic smaller than 35.39 is greater than 0.999. Therefore, the probability of getting a test-statistic greater than 35.39 is less than 0.001. As illustrated in the following video, we multiply by 2 and determine that the P-value is less than 0.002.

One final note ... as always, we should clarify when it is okay to use the t-test for testing \(H_0 \colon \rho = 0\)? The guidelines are a straightforward extension of the "LINE" assumptions made for the simple linear regression model. It's okay:

Our websites may use cookies to personalize and enhance your experience. By continuing without changing your cookie settings, you agree to this collection. For more information, please see our University Websites Privacy Notice.

Some Math for Bivariate Product Moment Correlation (not required for EPSY 5601):

Multiple the z scores of each pair and add all of those products. Divide that by one less than the number of pairs of scores. (pretty easy)

There is a strong relationship between the number of ice cream cones sold and the number of people who drown each month. Just because there is a relationship (strong correlation) does not mean that one caused the other.

One way researchers often express the strength of the relationship between two variables is by squaring their correlation coefficient. This squared correlation coefficient is called a COEFFICIENT OF DETERMINATION. The coefficient of determination is useful because it gives the proportion of the variance of one variable that is predictable from the other variable.

The intersection of a row and column shows the correlation between the variable listed for the row and the variable listed for the column. For example, the intersection of the row mathematics and the column science shows that the correlation between mathematics and science was .874. The footnote states that the three *** after .874 indicate the relationship was statistically significant at p

Most tables do not report the perfect correlation along the diagonal that occurs when a variable is correlated with itself. In the example above, the diagonal was used to report the correlation of the four factors with a different variable. Because the correlation between reading and mathematics can be determined in the top section of the table, the correlations between those two variables is not repeated in the bottom half of the table. This is true for all of the relationships reported in the table. .

Repeated measures correlation (rmcorr) is a statistical technique for determining the common within-individual association for paired measures assessed on two or more occasions for multiple individuals. Simple regression/correlation is often applied to non-independent observations or aggregated data; this may produce biased, specious results due to violation of independence and/or differing patterns between-participants versus within-participants. Unlike simple regression/correlation, rmcorr does not violate the assumption of independence of observations. Also, rmcorr tends to have much greater statistical power because neither averaging nor aggregation is necessary for an intra-individual research question. Rmcorr estimates the common regression slope, the association shared among individuals. To make rmcorr accessible, we provide background information for its assumptions and equations, visualization, power, and tradeoffs with rmcorr compared to multilevel modeling. We introduce the R package (rmcorr) and demonstrate its use for inferential statistics and visualization with two example datasets. The examples are used to illustrate research questions at different levels of analysis, intra-individual, and inter-individual. Rmcorr is well-suited for research questions regarding the common linear association in paired repeated measures data. All results are fully reproducible.

Figure 5. Comparison of rmcorr and simple regression/correlation results for age and brain structure volume data. Each dot represents one of two separate observations of age and CBH for a participant. (A) Separate simple regressions/correlations by time: each observation is treated as independent, represented by shading all the data points black. The red line is the fit of the simple regression/correlation. (B) Rmcorr: observations from the same participant are given the same color, with corresponding lines to show the rmcorr fit for each participant. (C) Simple regression/correlation: averaged by participant. Note that the effect size is greater (stronger negative relationship) using rmcorr (B) than with either use of simple regression models (A) and (C). This figure was created using data from Raz et al. (2005).

Copyright 2017 Bakdash and Marusich. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Statistical tests are a way of mathematically determining whether two sets of data are significantly different from each other. To do this, statistical tests use several statistical measures, such as the mean, standard deviation, and coefficient of variation. Once the statistical measures are calculated, the statistical test will then compare them to a set of predetermined criteria. If the data meet the criteria, the statistical test will conclude that there is a significant difference between the two sets of data.

Parametric statistical tests have precise requirements compared with non-parametric tests. Also, they make a strong inference from the data. Furthermore, they can only be conducted with data that adhere to common assumptions of statistical tests. Some common types of parametric tests are regression tests, comparison tests, and correlation tests.

One of the most common statistical tests is the t-test, which is used to compare the means of two groups (e.g. the average heights of men and women). You can use the t-test when you are not aware of the population parameters (mean and standard deviation).

It tests the difference between two variables from the same population (pre-and post-test scores). For example, measuring the performance score of the trainee before and after the completion of the training program.

The independent t-test is also called the two-sample t-test. It is a statistical test that determines whether there is a statistically significant difference between the means in two unrelated groups. For example, comparing cancer patients and pregnant women in a population.

ANOVA (Analysis of Variance) analyzes the difference between the means of more than two groups. One-way ANOVAs determine how one factor impacts another, whereas two-way analyses compare samples with different variables. It determines the impact of one or more factors by comparing the means of different samples.

MANOVA, which stands for Multivariate Analysis of Variance, provides regression analysis and analysis of variance for multiple dependent variables by one or more factor variables or covariates. Also, it examines the statistical difference between one continuous dependent variable and an independent grouping variable.

Correlation tests check if the variables are related without hypothesizing a cause-and-effect relationship. These tests can be used to check if the two variables you want to use in a multiple regression test are correlated.

It is a common way of measuring the linear correlation. The coefficient is a number between -1 and 1 and determines the strength and direction of the relationship between two variables. The change in one variable changes the course of another variable change in the same direction.

Non-parametric tests do not make as many assumptions about the data compared to parametric tests. They are useful when one or more of the common statistical assumptions are violated. However, these inferences are not as accurate as with parametric tests.

The chi-square test compares two categorical variables. Furthermore, calculating the chi-square statistic value and comparing it with a critical value from the chi-square distribution allows you to assess whether the observed frequency is significantly different from the expected frequency.

Before performing the study protocol, a level of significance is specified. The level of significance determines the statistical importance, which defines the acceptance or rejection of the null hypothesis.

You must decide if your study should be a one-tailed or two-tailed test. If you have clear evidence where the statistics are leading in one direction, you must perform one-tailed tests. However, if there is no particular direction of the expected difference, you must perform a two-tailed test.

Statistical tests and procedures are divided according to the number of variables that are designed to analyze. Therefore, while choosing the test , you must consider how many variables you want to analyze.

3a8082e126