Question

Each individual in a sample was asked to indicate on a quantitative scale how willing he or she was to spend money on the environment and also how strongly he or she believed in God ("Religion and Attitudes Toward the Environment," Journal for the Scientific Study of Religion [1993]: \(19-28\) ). The resulting value of the sample correlation coefficient was \(r=-.085 .\) Would you agree with the stated conclusion that stronger support for environmental spending is associated with a weaker degree of belief in God? Explain your reasoning.

Short answer

The correlation coefficient of -0.085 indicates a very week negative relationship between the strength of belief in God and support for environmental spending. It's not profound enough to conclude that stronger support for environmental spending is associated with a weaker degree of belief in God.

Step-by-step solution

Understand the Correlation Coefficient Value

The correlation coefficient, also known as r-value, is -0.085 in this case. It ranges from -1 to 1, where 1 indicates a strong positive correlation, -1 indicates a strong negative correlation, and 0 means no correlation. Negative sign suggests inverse relationship between variables.

Analyzing the Strength of Correlation

The absolute value of r is 0.085 which is very close to 0. This tells us that the correlation between the two variables, while negative, is very weak.

Interpret the Meaning

Despite the negative correlation, the strength of correlation is very weak to suggest that a person's belief in God significantly influences their tendency to support environmental spending. The absence of a strong correlation suggests that these two factors may largely be independent of each other.

Key concepts

Sample Correlation

The sample correlation measures the strength and direction of a linear relationship between two variables within a sample taken from a larger population. It's often denoted by the symbol 'r', and like our textbook example shows, it ranges from -1 to 1. A value of 'r' close to -1 indicates a strong negative correlation, meaning as one variable increases, the other tends to decrease. On the other hand, a value close to 1 suggests a strong positive correlation, where both variables tend to increase together. Values around 0, such as -0.085 in our case, imply little to no linear relationship.
In practical terms, if a survey found a correlation coefficient of -0.085 between environmental spending and belief in God, we'd interpret this as a very weak inverse relationship. This implies that as willingness to spend on the environment goes up slightly, belief in God might decrease slightly, or vice versa. Yet, this value is too weak to make definitive assertions about the relationship between these variables without further statistical analysis.

Statistical Significance

Statistical significance is key to interpreting research findings. It provides a measure of how likely it is that a result did not occur by random chance. Determining statistical significance involves using a p-value, which is calculated based on the sample size and the correlation coefficient among other factors.
In the example with environmental spending and belief in God, the correlation coefficient alone does not tell us if the relationship observed is statistically significant. To make such a claim, a p-value would need to be computed following hypothesis testing, and compared against a chosen significance level, typically 0.05. If the p-value is less than the significance level, the results are deemed statistically significant — suggesting that the observed correlation is unlikely to be due to chance. However, a weak correlation coefficient near zero often corresponds to a large p-value, implying that the result is not statistically significant.

Environmental Spending

Environmental spending refers to the allocation of funds for the conservation and improvement of the environment. This can encompass a broad range of activities, from pollution control to habitat conservation and investment in renewable energy. The willingness of individuals to spend money on environmental causes can be affected by various factors, including personal values, beliefs, economic status, and levels of environmental awareness.
In research, environmental spending is often studied to understand how different demographic or psychographic factors relate to environmental engagement. However, a weak correlation with a variable such as belief in God, as indicated by a small negative correlation coefficient, suggests that the hypothesis of religious belief significantly influencing environmental spending habits might not hold strong. Further research would be necessary to explore contributing factors fully.

Belief in God

Belief in God represents a person's faith or conviction in a higher power, which can profoundly impact various aspects of life, including ethical decision-making, social behavior, and personal values. The presence or absence of religious belief can influence an individual's worldview and actions significantly.
When studying the relationship between belief in God and other social or economic behaviors, such as environmental spending, researchers must be cautious to interpret correlations accurately. The weak negative correlation found in our textbook example suggests that on a shallow level, more belief in God might correlate with less spending on the environment, or vice versa. Still, it's essential to understand that correlation does not imply causation, and the weak coefficient indicates that any potential relationship is negligible and would likely not hold up to rigorous scientific scrutiny.