Chapter 4 Key Terms

Bidirectionality

The possibility that an observed correlation between any two variables, A and B, could be because changes in A cause changes in B, or because changes in B cause changes in A. If one variable influences the other, we would have no way of knowing which one is the cause and which one is the effect from correlational data.

• If musical performance is positively correlated with math scores, this could be because learning how to play music increases attention to numbers and math (e.g., fractions), OR, it could be because practicing math makes learning music easier. Simply measuring math performance and musical performance would not tell us, either way.

Cause-and-Effect Hypothesis

A testable declaration that changes in one conceptual variable cause changes in another.

Contralateral Motor Control ("Contra" = opposite, "lateral" = side)

This term refers to the way each cerebral hemisphere of the brain (left or right) controls voluntary muscle movement on the opposite side of the body.

Correlation Coefficient

A number between -1 and +1 representing the strength of a correlation between two variables, derived from data representing multiple pairs of measurements of those two variables. The absolute value of the coefficient reflects the strength of the relationship, and the sign of the coefficient reflects whether the relationship is direct (positive) or inverse (negative).

Correlational Hypothesis:

A testable statement declaring that two conceptual variables are predictably related to one another, so that the value of one can be used to predict the value of the other (within a range).

• The number of new pregnancies and the frequency of power outages across different locations are positively correlated.

Correlational Research/Study

A study designed to measure two conceptual variables in matched pairs, in order to test the hypothesis that they are predictably related to each other

Hypothesis

A sentence that declares or implies a testable relationship between two or more. The relationship can be correlational, cause-and-effect, or null.

Negative Correlation

A relationship between two conceptual variables such that as one increases, the other decreases.

Null Hypothesis

A statement that negates (nullifies) the research hypothesis. It simply says that the research hypothesis is NOT true.

• A research hypothesis might say that two variables, X and Y are positively correlated. The null hypothesis would be that X and Y are not correlated. If the research hypothesis is that X and Y are negatively correlated, the null hypothesis would still be that X and Y are not correlated. If a scientist hypothesizes that there is a cause-and-effect relationship between X and Y, the null hypothesis would be that there is no cause-and-effect relationship.

p-value (probability value)

The odds of getting whatever result we get (e.g., a particular correlation coefficient), assuming the null hypothesis is true. If the p-value is very low, the null hypothesis is probably not true, meaning the alternative (our research hypothesis) is supported. If the p-value is high, the odds of getting our results under the null hypothesis are high, so we can't reject the null hypothesis, and we have no support for the alternative (research hypothesis).

Positive Correlation

A relationship between two conceptual variables such that as one increases, so does the other.

Prediction

A statement about what will be observed in a study, based on the operational definitions of the variables being studied and assuming the research hypothesis is true.

Regression Line

In Correlational research, a straight line through the points on a scatterplot that is as close as possible to the maximum number of data points. The slope of the line and the average closeness of the data points to the line tell us about the strength and direction of the relationship between the variables, which are represented on the X and Y axes.

Theory

A unifying idea that explains multiple observations and has evidence to support it from multiple perspectives.

Third Variables

Any variable that could influence both conceptual variables in a correlational study, and therefore cause the two variables to correlate. Correlational research does not tell us anything about what these variables are, nor if they exist.

Strength of a Correlation

The predictability of the relationship between two variables, based on measurements of both variables (based on correlational data).

Scatterplot

A graph showing the relationship between paired measurements of variables (for example, height and weight), with the value of one variable on the x-axis and the value of the other on the y-axis. One point is drawn for each pair of measurements at the point on the graph where the x-value and y-value intersect.

Significant

Refers to a data set that would have had less than a 5% chance of occurring if the null hypothesis were true. ____ positive or negative correlations allow us to reject the null hypothesis and conclude that we have evidence to support a correlational hypothesis.

Why you shouldn’t use the word “proof”

1. Operational definitions are almost never perfect, meaning it may lack validity or reliability

2. scientific decisions are based on probability (odds of getting the observed results under the assumption the null hypothesis is true) → While there is a less than 5% chance that the null hypothesis is right, there’s still a likelihood that the research hypothesis is wrong

Is your research hypothesis supported?

1. Assume no real relationship exists (null hypothesis)

2. Consider size of sample and the assumption there’s no relationship → determine probability of producing observed result

   1. p-value (low = null hypo WRONG and research RIGHT, high = vice versa)

3. Apply a decision rule (p-value IS LESS THAN 0.05)