Data Analysis and Statistics - TCE Psychology (Tasmania)
“Describe and apply descriptive statistics and data-analysis techniques to psychological data.”
You need to organise and summarise data using measures of central tendency (mean, median, mode) and spread (range, standard deviation), describe distributions, choose the right graph, and interpret a correlation coefficient, all so you can draw and judge conclusions from a study.
What this dot point is asking
Collecting data is only half of research. This part of Module 1 is about turning raw numbers into a clear, defensible conclusion, and it is regularly examined alongside research methods.
Types of data
- Quantitative data are numerical (reaction time in milliseconds, number of words recalled). They are easy to analyse statistically and compare.
- Qualitative data are descriptive (interview transcripts, open responses). They are rich and detailed but harder to summarise objectively.
Quantitative data are further split into levels of measurement: nominal (categories, such as favourite colour), ordinal (ranked, such as finishing position) and interval or ratio (equal intervals, such as temperature or time). The level you have limits which summary is appropriate.
Descriptive statistics summarise and describe a data set (averages, spread, graphs). Inferential statistics use sample data to draw conclusions about a wider population and to judge whether a result is likely due to chance. TASC focuses mainly on descriptive statistics.
Measures of central tendency
- Mean: the arithmetic average; uses every score but is distorted by extreme outliers.
- Median: the middle score when ordered; resistant to outliers, useful for skewed data.
- Mode: the most frequent score; the only average usable for nominal data.
Measures of spread
The range is the highest score minus the lowest; quick but based on only two values. The standard deviation measures the average distance of scores from the mean: a small standard deviation means scores cluster tightly, a large one means they are widely spread. Reporting spread alongside an average is essential, because two groups can share a mean yet differ greatly in consistency.
A mean on its own can mislead. Two classes can both average 60 percent, but one with a standard deviation of 4 is consistent while one with a standard deviation of 25 has high and low extremes. Always pair central tendency with spread when describing data.
Distributions
In a normal distribution, scores form a symmetrical bell curve where the mean, median and mode coincide and most scores fall near the centre. Data can also be skewed: a positive skew has a tail of high scores pulling the mean above the median, while a negative skew has a tail of low scores. Recognising skew tells you that the median may describe the typical score better than the mean.
Graphing data
Choosing the right display matters. A bar graph compares separate categories (nominal or ordinal data). A histogram shows the frequency of a continuous variable with no gaps between bars. A line graph shows change over a continuous scale, such as time. A scatterplot shows the relationship between two variables and is the basis for correlation.
Interpreting correlation
A correlation coefficient (r) summarises the strength and direction of a relationship between two variables, running from minus 1 to plus 1. A value near plus 1 is a strong positive relationship (both rise together), near minus 1 is a strong negative relationship (one rises as the other falls), and near 0 means little or no linear relationship.
Read the value and its sign
A study reports between hours of sleep and number of errors on a task. The sign is negative and the magnitude is close to .
Describe direction and strength
This is a strong negative correlation: as sleep increases, errors decrease. The closeness of to tells you the relationship is strong and the points would cluster tightly around a downward line.
State the limit on the conclusion
It does not prove sleep causes fewer errors, because a third variable (such as overall health) could influence both, or the direction could be reversed. Correlation describes a relationship, not a cause.
A strong correlation never proves cause and effect. Only a controlled experiment can establish causation. Students lose marks by writing that one variable "causes" another from correlational data. State the direction and strength of the relationship, then note that a third variable or reverse causation may explain it.
Putting it together
When handed data in the exam, first identify the type and level of measurement, then pick the appropriate average and measure of spread, describe the shape of the distribution, and only then interpret what the numbers mean for the hypothesis. For relationships, describe the direction and strength of the correlation and resist any causal claim. This disciplined sequence is exactly what earns full marks on data-handling questions.
Exam-style questions
Questions in the style of TASC exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.
Practice7 marksA class of 9 students recorded the number of words recalled from a list: 4, 6, 6, 7, 8, 9, 10, 12, 50. Calculate the mean, median and mode. State which measure of central tendency best represents this data set and justify your choice.Show worked answer →
This is a data-handling item marked on Criterion 3. Calculate each statistic, then reason about which fits.
- Mean
- Sum the scores and divide by the count: , so the mean is words.
- Median
- Order the scores (already ordered) and take the middle of 9 values, the 5th score: the median is words.
- Mode
- The most frequent score is (it appears twice), so the mode is words.
- Best measure
- The median () best represents the data. The score of is an outlier that pulls the mean up to , well above almost every score, so the mean is misleading here. The median is resistant to outliers and reflects the typical recall.
Markers reward correct working, the right values, and a justification that names the outlier and the median's resistance to it.
Practice9 marksA researcher reports a correlation of between hours of study and exam marks, and presents the data in a scatterplot. Explain what this coefficient means, evaluate the use of a scatterplot for these data, and explain why the researcher cannot conclude that study time causes higher marks.Show worked answer →
This is an extended-response item marked on Criteria 3 and 7. Interpret, evaluate, then address causation.
- Interpreting the coefficient
- An of is a moderate-to-strong positive correlation: as study hours increase, exam marks tend to increase too. The sign () gives direction and the magnitude (toward ) gives strength.
- Evaluating the scatterplot
- A scatterplot is the correct display for two continuous variables; it shows the direction, the strength (how tightly points cluster around a line) and any outliers, which a single coefficient hides. A limitation is that it shows association only and can be misread as implying a line of cause.
- Why not causation
- Correlation cannot establish cause because the variables were measured, not manipulated. A third variable (such as motivation or prior ability) could drive both study time and marks, and the direction could even be reversed. Only a controlled experiment with a manipulated IV can support a causal claim.
Markers reward a correct reading of , a balanced evaluation of the scatterplot, and the standard correlation-is-not-causation reasoning applied to this study.