What Does It Mean to Have a Negative Relationship Between Two Variables?
How practice you decide if, indeed, there is a statistically significant relationship betwixt two variables in your written report? What does the p-value output in statistical software analysis mean? This commodity explains the concept and provides examples with computations and video tutorial.
What does a researcher mean if he says there is a statistically meaning human relationship betwixt two variables in his report? What makes the relationship statistically meaning?
These questions imply that a examination for correlation betwixt two variables was made in that particular study. The specific statistical examination could either be the parametric Pearson Product-Moment Correlation or the non-parametric Spearman'due south Rho exam.
Statistical Software Applications to Test a Statistically Significant Relationship
It is now easy to do computations using popular statistical software applications like the popular Statistical Package for the Social Sciences (SPSS) or Statistica and even using the data assay function of spreadsheets like the proprietary Microsoft Excel and the open-source only less popular Gnumeric.
In one case the statistical software has finished processing the data, You volition go a range of correlation coefficient values along with their corresponding p-values denoted by the letter p and a decimal number for a one-tailed and two-tailed examination. The p-value is the ane that matters when trying to judge whether there is a statistically significant human relationship between ii variables.
Confusing Definition of p-value
Many of my students in the statistics course I teach are confused most the meaning of p-value. I sympathise this dilemma considering the references I see online do not explain in easily understandable language the meaning of the p-value.
For instance, Investopedia, the acme resource that returns out of 83 million-plus searches on the pregnant of p-value, is challenging to understand for a offset researcher, an undergraduate, or even a graduate pupil for that affair. If you lot click the link I provided on the significant of p-value, yous will understand what I mean.
If yous understand the definition provided there, then there is no need for you lot to read the residue of the sections. Fifty-fifty with my advanced graduate schoolhouse education, I find the explanation vague if I would non exert an effort to try to empathise it.
Hence, I explain the meaning of p-value in the next section in the best way I tin in the simplest mode possible. I provide a detailed caption of what information technology means in the side by side section.
The Meaning of p-value
What does the p-value mean? This value never exceeds 1. Why?
The computer-generated p-value represents the estimated probability of rejecting the null hypothesis (Ho) that the researcher formulated at the beginning of the study. The nil hypothesis is stated in such a way that there is "no" difference betwixt the 2 variables being tested.
Therefore, this means that as a researcher, you should be articulate nigh what you want to test in the first place.
For example, your null hypothesis that will lend itself to statistical analysis should be written similar this:
H0: In that location is no relationship between the long quiz score and the number of hours devoted by students in studying their lessons.
If the computed value is exactly 1 (p = i.0), this means that the relationship is absolutely correlated. In that location is no dubiety that the long quiz score and the number of hours spent by students in studying their lessons are correlated.
That p-value means a 100% probability (read simply as 100 percent sure) that the long quiz score and the number of hours devoted past the students in studying their lessons are correlated. The greater the number of hours devoted by students in learning their courses, the higher their long quiz scores. As unproblematic as that.
Conversely, if the p-value is 0, this ways in that location is no correlation at all. It means that whether the students study or non, their long quiz scores are not afflicted at all.
Why in Reality the p-value of 1 is Non Possible
In reality, unless you are specializing in Physics, a p-value of one is hard to obtain when studying human behavior. In our instance, many factors or variables influence the long quiz score. Variables like the student's intelligence quotient, the teacher's instruction skill, the difficulty of the quiz, amongst others, touch on the score.
At present, this ways that the p-value should non be 1 or numbers greater than that. If yous get a p-value of more than 1 in your computation, that's nonsense. Your p-value, I repeat one time over again, should range betwixt 1 and 0.
To illustrate, if the p-value you obtained during the ciphering is equal to 0.5, this means that there is a l% chance that 1 variable is correlated to the other variable. In our case, nosotros tin can say that there is a 50% probability that the long quiz score is correlated to the number of hours spent by students in studying their lessons.
Or to put it simply, nosotros tin can say that there is a statistically meaning relationship between the long quiz scores of students and the number of hours that they spend studying their lessons.
Deciding Whether the Relationship is Significant
Suppose the probability in the case given higher up is p = 0.05. Is it proficient enough to say that there is a statistically significant human relationship between long quiz scores and the number of hours spent past students studying their lessons?
The answer is NO. Why?
In today's standard dominion or convention in the earth of statistics, statisticians prefer a significance level denoted by blastoff (α) as a pre-chosen probability for significance. The value for significance is commonly fix at either 0.05 (statistically significant) or 0.01 (statistically highly significant). These numbers stand for 5% and 1% probability, respectively.
Comparing the computed p-value with the pre-called probabilities of 5% and 1% volition help you decide whether the relationship between the two variables is meaning or not. If, say, the p-values you lot obtained in your computation are 0.5, 0.iv, or 0.06, you should accept the null hypothesis. That is if you ready alpha at 0.05 (α = 0.05). If the value you got is beneath 0.05 or p < 0.05, then you lot should accept your alternative hypothesis.
In the above example, the culling hypothesis that should be accepted when the p-value is less than 0.05 volition be:
H1:There is a relationship betwixt the long quiz score and the number of hours devoted past students in studying their lessons.
The strength of the human relationship is indicated past the correlation coefficient or r values. Guilford (1956) suggested the following categories as guide:
| r-value | Interpretation |
| < 0.twenty | slight; almost negligible human relationship |
| 0.20 – 0.40 | depression correlation; definite only pocket-size relationship |
| 0.xl – 0.70 | moderate correlation; substantial relationship |
| 0.70 – 0.ninety | high correlation; marked relationship |
| > 0.90 | very high correlation; very dependable relationship |
Computation of Correlation in SPSS
If you want to learn about how to utilise SPSS in computing correlations, the 8-minute tutorial by Dr. Bogdan Kostic below on the correlation between Intelligence Quotient (IQ) and Course Point Average (GPA) will guide you. He demonstrates in detail how the data are encoded in SPSS, how the labels are written, and the process of statistical test selection. In this instance, the correlation between IQ and GPA using Pearson's product-moment correlation with the accompanying computer output. This video volition further strengthen your knowledge on how to make up one's mind if in that location is a significant relationship between ii groups of variables.
More than examples and demonstrations on how to find out if in that location is a statistically pregnant human relationship between variables are given in the two articles beneath. These articles provide example computer outputs and how these are interpreted.
How to Use Gnumeric in Comparing Two Groups of Data
Middle Rate Assay: Example of t-test using MS Excel Analysis ToolPak
More Easy-to-Follow Tips
For very easy-to-follow tips on how to select the appropriate statistical tests for your report, run across my eBook on statistics at the middle of the page in Simplyeducate.me's eBook shop.
Reference:
Guilford, J. P., 1956. Fundamental statistics in psychology and education. New York: McGraw-Hill. p. 145.
© 2014 May 29 P. A. Regoniel
Updated 13 Nov 2020
Source: https://simplyeducate.me/2014/05/29/statistically-significant-relationship/
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