Question

Discuss the difference between correlation and causation and the difference between statistical and practical significance. Please give examples of each to help define each concept.

Answer 1

PART A

Two or more variables considered to be related, in a statistical context, if their values change so that as the value of one variable increases or decreases so does the value of the other variable (although it may be in the opposite direction).
For example, for the two variables "hours worked" and "income earned" there is a relationship between the two if the increase in hours worked is associated with an increase in income earned. If we consider the two variables "price" and "purchasing power", as the price of goods increases a person's ability to buy these goods decreases (assuming a constant income).

Correlation is a statistical measure (expressed as a number) that describes the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable. Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a causal relationship between the two events. This is also referred to as cause and effect.

Theoretically, the difference between the two types of relationships are easy to identify — an action or occurrence can cause another (e.g. smoking causes an increase in the risk of developing lung cancer), or it can correlate with another (e.g. smoking is correlated with alcoholism, but it does not cause alcoholism). In practice, however, it remains difficult to clearly establish cause and effect, compared with establishing correlation.

PART B

In Statistical Significance the hypothesis testing procedure determines whether the sample results that you obtain are likely if you assume the null hypothesis is correct for the population. If the results are sufficiently improbable under that assumption, then you can reject the null hypothesis and conclude that an effect exists. In other words, the strength of the evidence in your sample has passed your defined threshold of the significance level (alpha). Your results are statistically significant.

While statistical significance relates to whether an effect exists, practical significance refers to the magnitude of the effect. However, no statistical test can tell you whether the effect is large enough to be important in your field of study. Instead, you need to apply your subject area knowledge and expertise to determine whether the effect is big enough to be meaningful in the real world. In other words, is it large enough to care about?

The difference between a sample statistic and a hypothesized value is statistically significant if a hypothesis test indicates it is too unlikely to have occurred by chance. To assess statistical significance, examine the test's p-value. If the p-value is less than a specified significance level (α) (usually 0.10, 0.05, or 0.01), you can declare the difference to be statistically significant and reject the test's null hypothesis.

For example, suppose you want to determine whether the thickness of car windshields is larger than 4mm, as required by safety rules. You take a sample of windshields and conduct a 1-sample t-test. If the test produces a p-value of 0.001, you declare statistical significance and reject the null hypothesis because the p-value is less than α. You conclude in favor of the alternative hypothesis: that the windshield thickness is greater than 4mm. But if the p-value equals 0.50, you cannot claim statistical significance. You do not have enough evidence to claim that the average windshield thickness is larger than 4mm.