Types of Statistics
Descriptive statistics are numerical data used to measure and describe characteristics of groups, and this includes measures of variation. Therefore, descriptive statistics describe the data📊.
Inferential statistics provide a way to see validity drawn from the results of the experiment🧪🔬. Inferential statistics tell what the data means.
Measures of Central Tendency
Interpreting and constructing graphs📈 and calculating simple descriptive statistics….
The measures of central tendency are median, mean, and mode.
Median is the middle score of distribution. Mean is the average of a set of scores. Mode is the most frequently recurring score.
If two scores appear the most frequently, the distribution is bimodal. If three or more scores appear most frequently, the distribution is multimodal.
For example, take this sets of numbers here:
5, 10, 5, 7, 12, 15, 18
The median is the middle of the data set when the numbers are in order so it is 10.
The mode is 5 because it occurs the most.
The mean is (5 + 10 + 5 + 7 + 12 + 15 + 18)/7 = 10.286
Measures of Variation
Standard deviation is a measure of variability mentioning scores of distribution and the mean. It is used to assess how far the values are spread below and above the mean.
The Z score tells how far a number is below or above the mean in terms of standard deviation.
Correlation coefficient describes how well two variables are correlated. The correlation coefficient ranges from -1 to +1. The closer to -1 or +1, the stronger the correlation.
Positive correlation shows that as one variable increases ⬆️, the other variable increases ⬆️ For example, a positively correlated group may show that as height increases, weight increases as well.
Image courtesy of Expii.
Negative correlation shows that as one variable increases ⬆️, the other decreases ⬇️. An example of a negative correlation could be how as the number of hours of sleep increases, tiredness decreases.
Image courtesy of Expii.
No correlation shows that there is no connection❌ between the two variables. An example of no correlation could be IQ and how many pairs of pants an individual owns.
Image courtesy of Expii.
Remember, correlation does not imply causation. You must run an experiment to prove there is causation.
Frequency distribution is a breakdown of how the scores fall into different categories or ranges. Normal distribution shows how traits are distributed throughout a population usually with the use of a bell 🔔 curve.
There are also positive skews👍 and negative skews👎. Graph a below is positively skewed (aka skewed to the right) because the direction of the skew is going in a positive direction. Letter c is negatively skewed (aka skewed to the left) because the direction of the skew is pointing in the negative direction.
It might be hard to remember which way the skew is. If the tail on the right is longer, like it is in a, then it's a skew to the right. If the tail on the left is longer, like it is in c, then it's a skew to the left.
When the distribution is skewed to the right, the mean is greater than the median. When the distribution is skewed to the left, the median is greater than the mean.
Image courtesy of ResearchGate.
The normal curve, or (b) in the above image, is the only one you have to really be familiar with for this course. There are two important values that you should memorize: 68% and 95%.
Image from Myers' AP Psychology Textbook; 2nd Edition
This is a normal curve that includes data about intelligence📖. Basically, 68% of the data falls within one standard deviation about the mean. Here, one standard deviation is equivalent to 15, so the data falls between 85 and 115, or +- 15 points of 100.
95% of the data falls within two standard deviations about the mean. Since 2 standard deviations is equal to 30, the data falls between 70 and 130, or +-30 points of 100.
Another term that you should be somewhat familiar with is statistical significance, or the likelihood that something occurs by chance😲. If something is statistically significance, it did not occur by chance (some outside factor influenced the data). If something isn't statistically significant, it occurred completely by chance. To determine this, you would compare the mean of the control group and the mean of the experimental group.
The following question is taken from the College Board website (2017 AP Exam - Part B of #1
A study was conducted to investigate the role of framing on concern for healthy eating🍏. Each participant (N = 100) was randomly assigned to one of the two conditions. In the first condition, the participants read an article indicating that obesity is a disease🦠. Participants in the second condition read an article indicating that obesity is the result of personal behaviors and decisions.
Participants were asked to indicate how important it would be for them to eat a healthy diet. Scores ranged from 1 (not very important) to 9 (very important). The results are presented in the table below.
Mean Score - Concern for Healthy Eating
Table Courtesy of College Board
Operationally define the dependent variable.
What makes the study experimental rather than correlational?
What is the most appropriate conclusion the researchers can draw about the relationship between the variables in the study?
The scoring guidelines
provide the rubric for this question. You should be able to answer all three parts. If not, just go through this unit’s guides one more time and you’ll nail this FRQ.
🎥Watch: AP Psychology - Statistics in Psychology