Which of the following is a correct representation of a strong negative correlation?
I. Correlations (Video Lesson 7 I) (YouTube version)
II. Scatterplots (Video Lesson 7 II) (YouTube version)
A. Scatterplots can show the strength of the relationship between two variables 1. Weak relationships will have a wide scattering of the plots
2. Strong relationships will have a minimal scattering of the plots
B. Scatterplots can show the direction or type of the relationship between two variables1. Positive Correlationboth factors vary in the same direction as one factor increases, the other increases
2. Negative Correlationboth factors vary in opposite directions as one factor increases, the other decreases
3. Zero or Neutral Correlationthe two factors show no relationship to one another
III. The Pearson Product Moment Correlation (Correlation Coefficient) (Video Lesson 7 III) (YouTube version) (Correlation Calculation - YouTube version) (mp4 version)
IV. Determining Significance (Video Lesson 7 IV) (YouTube version)
A. The Coefficient of Determination
Coefficient of Determination = r2
B. The R TableThe R Table is located in its entirety in Appendix A in the back of the text book. A shortened version is also available at the bottom of this lecture. It starts on page 435 and gives the critical R values based on degrees of freedom of your sample, the level of significance of the statistical test, and whether your hypothesis is one- or two-tailed. These three factors plus the critical R values are represented in the R Table and will be explained one at a time. 1. Degrees of Freedom. The term degrees of freedom refers to the number of scores within a data set that are free to vary. In any sample with a fixed mean, the sum of the deviation scores is equal to zero. If your sample has an n equal to 10. The first 9 scores are free to vary but the 10th score must be a specific value that makes the entire distribution equal to zero. Therefore in a single sample the degrees of freedom would be equal to n - 1. The degrees of freedom for a correlation is slightly different because n equals number of pairs not simply sample size. Therefore, the degrees of freedom for a correlation in n - 2. So to calculate the degrees of freedom you simply take the number of pairs and subtract two. For our data set of depression and self-esteem scores the degrees of freedom are calculated the following way: df = n -2 df = 8 - 2 df = 6 The R Table shows the degrees of freedom values in the far left column as shown below: Levels of Significance for a One-Tailed Test Levels of Significance for a Two-Tailed Test
The table continues 2. One- or Two-tailed hypotheses. The number of tails of a hypothesis predict the direction of the hypothesis. This concept will be discussed in greater detail in chapter 11. For now, you should know that if a correlation hypothesis is simply predicting an effect without predicting either a negative or positive direction of that effect, it is considered a Two-Tailed hypothesis. If the hypothesis is predicting either a negative or positive direction then it is a One-Tailed hypothesis. Since our hypothesis as stated predicts a negative correlation it is a One-Tailed Test. The two levels of hypothesis tests are highlighted below: Levels of Significance for a One-Tailed Test Levels of Significance for a Two-Tailed Test
3. Levels of Significance. The levels of significance or "p values" will also be discussed in greater detail in chapters 11, 12, and 13. For now you should simply know that a level of significance at .05 is equivalent to p = .05 which means that there is a 95% probability of statistical significance (1.00 - 0.05 = 0.95 or 95%) between your two variables. The .05 value is considered standard in science. Levels of significance that are smaller show greater significance and values that are larger show less significance. This value must be given to you in the problem. For our example let's use a p = .05. The table below shows the highlighted levels of significance: Levels of Significance for a One-Tailed Test Levels of Significance for a Two-Tailed Test
4. Critical R Values. Critical values are threshold values for significance. Your calculated r value must exceed the critical r value in the R Table to be considered significant. The table below shows the highlighted critical r values: Levels of Significance for a One-Tailed Test Levels of Significance for a Two-Tailed Test
Now let's put it all together. The table below shows the criteria of our example to determine if our calculated r value of is significant: Levels of Significance for a One-Tailed Test Levels of Significance for a Two-Tailed Test
Since our calculated r = -0.9244 We conclude that our correlation is significant. *Note that the final cumulative percent score should equal 100% Additional Links about the Concepts that might help: Which of the following represent a strong negative correlation?A correlation coefficient of -0.8 or lower indicates a strong negative relationship, while a coefficient of -0.3 or lower indicates a very weak one.
Is 0.9 A strong negative correlation?The magnitude of the correlation coefficient indicates the strength of the association. For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association.
Is negative 0.5 a strong correlation?Negative correlation is measured from -0.1 to -1.0. Weak negative correlation being -0.1 to -0.3, moderate -0.3 to -0.5, and strong negative correlation from -0.5 to -1.0.
Is 0.7 A strong or weak correlation?The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables. Pearson r: r is always a number between -1 and 1.
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