Descriptive and Correlational Statistics
Descriptive and correlational statistics help interpret the relationship, or relatedness, between observable variables.
Learning Objective

Distinguish between correlation and causation in psychological research
Key Points
 Descriptive statistics describe how the data looks; however these statistics are not used to make any inferences from the collected data in relation to any population outside of the sample group.
 Correlational statistics measure the strength of the relationship between two variables, indicating that the two variables are connected.
 A correlational study shows only the relationship, or relatedness, between two variables. This is different than causation, where one variable causes the other.
 Tools used for descriptive statistics include quantitative measures such as the mean, median, and mode, as well as a distribution curve.
 If the mean is greater than the median, and the median is greater than the mode, the distribution will be positively skewed. However, if the mean is less than the median, and the median is less than the mode, then the distribution will be negative skewed.
 The normal distribution curve exists when the mean and median are close together. For an ideal normal distribution, the mean is equal to the median and the mode.
Terms

experiment
A test under controlled conditions made to either demonstrate a known truth, examine the validity of a hypothesis, or determine the efficacy of something previously untried.

correlation
One of the several measures of the linear statistical relationship between two random variables, indicating the strength of the relationship but not necessarily the causation.

skewed
Biased or distorted information.
Example
 Research has shown that alcohol dependence correlates with depression. This could mean that the more alcohol people consume, the more depressed they become; on the other hand, it could mean that the more depressed people become, the more likely they are to consume alcohol. Correlation does not necessarily prove causation.
Full Text
Descriptive and correlational statistics are used in psychology to describe data and illustrate the results. As the name suggests, descriptive statistics describe how the data looks. These statistics are not used to make any inferences from the collected data in relation to any population outside of the sample group. Tools used for descriptive statistics include quantitative measures such as the mean, median, and mode, as well as a distribution curve.
Correlational statistics, however, measure the strength of the relationship between two variables, indicating that the two variables are connected and not unrelated. Despite measuring the strength of the relationship between two variables, correlational statistics do not prove that one variable causes the other to occur.
Correlation Versus Causation
A correlational study shows only the relationship, or relatedness, between two variables which have been quantified as measurable numbers. This is different than causation, where one variable is found to cause the other. The attributes of correlations include strength and direction, known as the degree of relation, being positive (both variables increase or decrease together, up to a value of +1), negative (one variable increases while the other decreases, down to a value of 1), or unrelated (a random relationship between the variables, a value of 0). The closer the degree of relation to a 1 or +1, the stronger the relationship between the two variables (regardless of a positive or negative value), whereas the closer the degree of relation is to 0, the weaker the relationship.
A correlational study can only describe or predict behavior, but cannot explain the behavior. This is because other variables may be shown to be the actual cause of the occurrence. Only scientific experiments can prove causation. As an example of a correlational study, research has shown that alcohol dependence correlates with depression. This could be interpreted to imply that the more alcohol that people consume, the more depressed they become. However, it could also be interpreted to imply that the more depressed people become, the more likely they are to consume alcohol.
Data Distribution Shape
The mean, median, and mode can impact the shape of the distribution. When the three are equivalent, or approximately equivalent, the distribution is considered normal. But when the three are unequal, the distribution can become positively or negatively skewed.
Mean, Median, and Mode of a Data Set
The mean is the average of the values in a data set, and can only be computed for interval and ratio data. The median is the middle value of the data set. If the data set is an odd number, then it is the middle value once the data values are ranked. If the data set is made up of an even number of values, then the two middle values should be averaged to find the median. The median can be computed for ordinal, interval, and ratio data. The mode is the value which occurs the most in the data set. It can be on value, considered to be single modal, or can be more than one value, and thus multimodal.
Normal Distribution and Skewed Curve of a Data Set
The normal distribution curve exists when the mean and median are close together. For an ideal normal distribution, the mean is equal to the median, as well as the mode . The normal distribution is expressed in terms of standard deviation around the mean, where 68% of values lie within one standard deviation of the mean, and where approximately 96% of the values lie within two standard deviations of the mean.
Normal Curve
The normal, or Gaussian, distribution of values. Also known as the bell curve. This occurs when the mean, median, and mode are equivalent, or approximately equivalent.
If the mean is greater than the median, and the median is greater than the mode, the distribution will be positively skewed. However, if the mean is less than the median, and the median is less than the mode, then the distribution will be negatively skewed .
Example of Skewness
When the mean, median, and mode are unequal, the normal curve can become skewed in either a negative or positive direction depending on their values in relation to each other.
Key Term Reference
 attribute
 Appears in these related concepts: Features and Attributes of a Product, Managers as Leaders of Change, and Introduction to Industrial and Organizational Psychology
 causation
 Appears in these related concepts: Analyzing Data and Drawing Conclusions, Descriptive Research, and Correlational Research
 dependence
 Appears in these related concepts: Defining Motivation, Incentive Theory of Motivation and Intrinsic vs. Extrinsic Motivation, and SubstanceRelated and Addictive Disorders
 inference
 Appears in these related concepts: Relationships and Families in Adulthood, History of Cognition, and Reasoning and Inference
 interval
 Appears in these related concepts: The Intermediate Value Theorem, Consonance and Dissonance, and Interval Notation
 mores
 Appears in these related concepts: Folkways and Mores, Counterculture, and Human Sexuality and Culture
 ordinal
 Appears in these related concepts: DistributionFree Tests, Defining Utility, and Describing Qualitative Data
 population
 Appears in these related concepts: Applications of Statistics, The Functionalist Perspective on Deviance, and Quorum Sensing
 quantitative
 Appears in these related concepts: Preparing the Research Report, Overview of the IMRAD Model, and Math Review
 ratio
 Appears in these related concepts: The Importance of Productivity, Basic Descriptive Statistics, and Schedules of Reinforcement
 sample
 Appears in these related concepts: Identifying Product Benefits, Surveys, and Basic Inferential Statistics
 set
 Appears in these related concepts: Sequences, Introduction to Sequences, and Sequences of Mathematical Statements
 standard deviation
 Appears in these related concepts: Using the Normal Curve, Interpreting the Standard Deviation, and Variance
 statistics
 Appears in these related concepts: Communicating Statistics, Population Demography, and Understanding Statistics
Sources
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