Source: General Psychology, The Ohio State University
Difficulty: Introductory | Prerequisites: Parts 1 and 2 (Scientific Method, Descriptive Research, Correlational Research, Experiments)
Tags: descriptive statistics, inferential statistics, mean, median, mode, central tendency, measures of variation, range, standard deviation, normal distribution, bell curve, p-value, statistical significance, ethics, IRB, Institutional Review Board, informed consent, confidentiality, debriefing, animal testing
You have covered how psychologists collect data (descriptive methods, correlations, experiments). This section covers what they do with that data and the ethical rules they follow while collecting it. Statistics give researchers the tools to summarise findings and decide whether results are meaningful or just due to chance. Ethics ensure that the pursuit of knowledge does not come at the cost of participants' wellbeing. Both topics are foundational: statistics appear in every research paper you will ever read, and ethical guidelines shape every study that gets approved.
Descriptive statistics (mean, median, mode, range, standard deviation) summarise your data. Inferential statistics (especially the p-value) tell you whether your results are likely real or just a product of chance. Ethical research requires IRB approval, informed consent, confidentiality, and debriefing, with additional considerations for animal subjects.
Descriptive statistics
Statistics that describe, summarise, or display your data. Common tools include graphs, histograms, pie charts, and measures of central tendency.
In simple terms, these are the numbers and pictures that help you see what your data looks like.
Central tendency
A single value that represents the centre or typical value of a dataset. The three measures of central tendency are the mean, median, and mode, each offering a slightly different perspective.
In simple terms, central tendency answers "what is a typical score in this group?"
Mean
The average of the data: the sum of all values divided by the number of values.
In simple terms, add everything up and divide by how many there are.
Median
The midpoint of a frequency distribution, such that there is an equal chance of a score falling above or below it.
In simple terms, line up all the scores from lowest to highest and pick the one in the middle.
Mode
The value that occurs most frequently in the dataset.
In simple terms, it is the most popular score.
Measures of variation
Statistics that tell you how similar or different the scores in a group are. They describe the spread rather than the centre.
In simple terms, central tendency tells you where the middle is; variation tells you how tightly the scores cluster around that middle.
Range
The difference between the highest and lowest scores in a dataset.
In simple terms, subtract the smallest number from the largest.
Standard deviation
A measure of how much scores vary from the mean. A small standard deviation means scores are clustered close to the mean; a large one means they are spread out.
In simple terms, it tells you whether most people scored near the average or all over the place.
Normal distribution (bell curve)
A bell-shaped, symmetrical curve in which the mean, median, and mode are all the same value. Most scores cluster near the centre, with fewer and fewer scores at the extremes.
In simple terms, it is the classic "bell curve" where most people are average and fewer people are at the very top or bottom.
Inferential statistics
Statistics that allow a researcher to state with confidence whether the difference between experimental and control groups is real and not simply due to chance.
In simple terms, these are the tools that help you decide "is this finding meaningful, or could it be a fluke?"
P-value
The probability that your results are due to chance. A p-value of 0.05 means there is a 5% likelihood that the results happened by chance. Lower is better.
In simple terms, if p is below 0.05, most psychologists consider the result statistically significant.
Institutional Review Board (IRB)
A committee that reviews research proposals to ensure they meet ethical standards. The IRB makes sure research will not cause unnecessary physical or psychological harm and that the study is conducted safely.
In simple terms, this is the ethics committee that must approve a study before it can go ahead.
Informed consent
The ethical requirement that participants are told what the study involves and agree to participate voluntarily, before the study begins.
In simple terms, you must tell people what they are signing up for and give them a real choice about whether to take part.
Debriefing
The process of explaining the true purpose of a study to participants after it is completed, especially if any deception was involved.
In simple terms, after the study ends, you tell participants what was really going on.
Confidentiality
The ethical obligation to keep participants' data private and not disclose their identity or responses without permission.
In simple terms, what participants share stays between them and the research team.
Descriptive statistics do not tell you whether a finding is significant. They tell you what the data looks like.
Measures of central tendency:
Mean: Most commonly used. Sensitive to extreme scores (outliers), which can pull it up or down.
Median: Resistant to outliers. Useful when a dataset is skewed.
Mode: The only measure that can be used with categorical data (e.g., favourite colour). A dataset can have more than one mode.
Each gives a slightly different view of the same dataset, which is why researchers often report more than one.
Course example (Assignment 6.2):
Mean: approximately 81.1
Median: 82.1
Mode: 79.1
Because these three values are close but not identical, the distribution is roughly normal but not perfectly symmetrical.
Measures of variation:
Range: Simple but crude. One extreme score can make the range misleadingly large.
Standard deviation: More informative. Calculated by finding the mean, computing each score's deviation from the mean, squaring those deviations, averaging the squared deviations, and taking the square root.
If the standard deviation is small, scores are tightly clustered around the mean.
If it is large, scores are spread out.
Inferential statistics help researchers determine whether the difference between the experimental and control groups is statistically significant (unlikely to have occurred by chance).
The key metric is the p-value:
A p-value of 0.05 (5%) is the conventional threshold. If p ≤ 0.05, the result is considered statistically significant.
Lower p-values indicate stronger evidence against the result being due to chance.
In a normal distribution, the mean, median, and mode all fall at the same point, and the curve is perfectly symmetrical.
Standard deviation calculation (step by step):
Find the mean of the dataset.
Subtract the mean from each score to get the deviation.
Square each deviation.
Sum the squared deviations.
Divide by the number of scores (for a population) or by n - 1 (for a sample).
Take the square root of the result.
Formula: SD = √[ Σ(x - mean)² / n ]
Normal distribution curve:
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Mean
(= Median = Mode)
In a normal distribution, roughly 68% of scores fall within one standard deviation of the mean, 95% within two, and 99.7% within three.
Psychological research often involves human participants who may be vulnerable, deceived, or placed in stressful situations. Ethical guidelines exist to protect participants from harm while still allowing meaningful research.
Every institution that conducts research with human subjects has an IRB.
The IRB reviews proposals before research begins and ensures:
The study will not cause unnecessary physical or psychological pain or trauma.
The study meets safety standards.
The benefits of the research outweigh any potential risks.
Course example (Assignment 6.3): The University of Michigan's IRB oversees human subject research in their medical school. They provide guidance on the current state of knowledge, help create consent documents, and provide background information for participants.
Voluntary participation: Nobody can be forced to take part in a study.
Informed consent: Participants must be told what the study involves before they agree to participate.
Confidentiality: Participant data and identity must be kept private.
Deception and debriefing: If deception is used (and only when necessary), participants must be fully debriefed afterward, with the true nature of the study explained.
Animal research in psychology follows separate ethical guidelines. The key principle is that animal subjects should be treated humanely, and research should only be conducted when the potential benefits justify the use of animals.
Standard deviation is used in education (grading on a curve), finance (measuring investment risk), and manufacturing (quality control). P-values appear in medical research every time a new drug or treatment is tested. IRB oversight is required at every university and hospital that conducts research, and has been shaped by historical failures of research ethics, including the Tuskegee syphilis study and the Stanford prison experiment.
Students often treat the mean as the only or best measure of central tendency. In skewed datasets, the median is more informative because it is not affected by outliers.
A common error is thinking that a p-value of 0.05 means there is a 95% chance the hypothesis is correct. It means there is only a 5% chance that the observed results are due to chance, assuming the null hypothesis is true. Those are different statements.
Students sometimes assume that a small standard deviation is always "good." Whether it is desirable depends on context; it simply means the data points are close together.
Students may think that informed consent makes deception in research impossible. Deception is permitted in some studies (when no other method will work), but debriefing is then mandatory.
⚠️ Know how to calculate and interpret the mean, median, and mode. Exam questions may give you a dataset and ask for all three.
⚠️ Understand what standard deviation tells you about a dataset and be able to explain the difference between a small and large standard deviation.
⚠️ Be able to interpret a p-value. Know that p ≤ 0.05 is the conventional threshold for statistical significance.
⚠️ Know the role of the IRB and be able to name the core ethical principles (voluntary participation, informed consent, confidentiality, debriefing).
⚠️ Understand the relationship between the mean, median, and mode in a normal distribution (they are all equal).
True or False: In a normal distribution, the mean, median, and mode are all different values.
Fill in the blank: A p-value of 0.05 means there is a __________% chance the results are due to chance.
True or False: The range is a more informative measure of variation than the standard deviation.
Fill in the blank: The ethics committee that must approve research before it begins is called the __________.
True or False: If a study involves deception, participants must be debriefed after the study.
Answers: 1. False (in a normal distribution, all three are the same). 2. 5. 3. False (standard deviation is more informative; range only uses two data points). 4. Institutional Review Board (IRB). 5. True.
Q: A class of 10 students scores the following on a quiz: 70, 75, 80, 80, 82, 85, 88, 90, 92, 98. What are the mean, median, and mode?
A: Mean = (70+75+80+80+82+85+88+90+92+98) / 10 = 84.0. Median = the average of the 5th and 6th scores = (82+85) / 2 = 83.5. Mode = 80 (appears twice).
Q: What does a small standard deviation tell you about a dataset?
A: It tells you that most scores are clustered close to the mean, with relatively little variation between them.
Q: A researcher reports a p-value of 0.03. Is this result statistically significant, and what does it mean?
A: Yes, it is statistically significant (below the 0.05 threshold). It means there is only a 3% probability that the observed difference between groups is due to chance.
Q: Why is informed consent important in psychological research?
A: Informed consent ensures that participants understand what the study involves and agree to take part voluntarily. It protects participants' autonomy and wellbeing, and it is a core ethical requirement enforced by IRBs.
Q: A researcher studying stress tells participants the study is about "memory." After the study, she explains the true purpose. Name the two ethical concepts involved.
A: Deception (misleading participants about the study's purpose) and debriefing (explaining the true purpose after the study ends).
Statistics connect to every research-based topic in the course. Any time a textbook says "researchers found that..." there is a p-value behind that claim. The ethics section connects to the history of psychology (earlier research had far fewer ethical safeguards) and to clinical and social psychology, where research often involves sensitive topics and vulnerable populations. The concept of the normal distribution reappears in intelligence testing and personality assessment.
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