The definitions and usage of validity and reliability differ subtly across different disciplines, with exact definitions differing depending on context. In statistics, as well as sciences that use statistics to empirically reach conclusions, both the validity and reliability of the information being presented need to exist in order for conclusions to be made, or in order to support or reject a hypothesis.
Validity is a test of whether or not the information at hand is measuring the correct things.
Validity is perhaps the most important factor in social science and statistics, as the social sciences often struggle with how variables are correlated with one another, and if any two correlated variables can actually prove causation (that B happened because of A).
A parable often used to demonstrate validity is that of ice cream and crime. The parable goes as follows: In Central Park in New York City, a social scientist and his statistician friend decide to try to observe the causes of crime in the park. After taking in a variety of factors, they notice a trend: the more ice cream sales present in the park, the more crime that would happen. As ice cream sales approached zero, the crime rate dropped. As ice cream sales peaked, the crime rate would shoot up accordingly. Is ice cream a valid measurement of crime rates?
If this measurement is valid, then the researchers could say ice cream causes crime, though most would look at the argument and see it as ridiculous. Ice cream sales then are not valid measurements of crime. A closer examination found that ice cream sales and crime were correlated because of weather patterns – on rainy days, no ice creams were bought, and fewer people were at the park, resulting in fewer crimes in the park. On days with nice weather, more people were in the park buying ice cream, and the increase in people in the park led to more crimes being committed.
Reliability is a simpler concept, but just as necessary for a conclusion to be supported. Reliability can most simply be stated as consistency, both in the methods used when conducting an experiment as well as the results received.
In order for test results to be reliable, it would mean that every time you conduct the same test, you get the same results. Typically, in order to produce reliable results, researchers and scientists need to perfectly control all the conditions of their test, ensure consistency between tests, and to allow them to measure how different variables affect their experiment.
In order for an experiment to have its conclusions considered, it must pass both tests of validity and reliability. An experiment can have reliable results without being valid if that experiment continues to provide the same results but is measuring something other than what the researchers intend, or is measuring what the researcher intends incorrectly. An example would be a broken measuring instrument that gives the same wrong measurement each time. The experiment at hand is reliable because the same results are being produced, but it is not valid.
An experiment can never be valid if it is not reliable first. If every time an experiment is run or a measurement taken is different, a researcher can conclude that they are not measuring what they intend to measure. Once an experiment has solved both the validity problem (to be reasonably sure they are testing the right thing) and the reliability issue (that each time they test it, they get the same results), then that research can begin to draw conclusions based on their experiment and share their conclusions for other researchers to build upon.