07. SPSS Classroom - Analyzing and Reporting One Sample T Test in SPSS

A one-sample t test is the go-to method when researchers have a single sample and want to check whether its mean matches a known population benchmark—like a company’s advertised product lifetime or a school’s claimed graduate salary. It matters because it turns a claim about “average equals X” into a statistical decision using a t statistic and a p-value, letting analysts quantify whether observed differences are likely due to chance.

The session frames the one-sample t test as the sample-based counterpart to the z test. Both rely on the same general logic—comparing a sample mean to a standard value—but they differ in assumptions. Z tests typically require known population parameters (mean and standard deviation), while t tests are used when those population values aren’t known exactly. In real-world settings, analysts often only have a benchmark value (for example, a claimed mean) and must estimate variability from the sample, making the t test more practical. Sample size guidance is also given: results from t tests tend to align closely with z tests when sample sizes are around 30–40, so the method doesn’t demand huge datasets.

Three t-test variants are introduced to clarify when each applies: one-sample t test (one sample vs. a population mean), independent-samples t test (two independent groups), and dependent (paired) t test (the same subjects measured twice). The focus then narrows to the one-sample t test, used for questions like whether regional per capita income equals a national average, whether a product’s household penetration meets a target level, or whether manufacturing dimensions have drifted from original specifications.

Validity hinges on assumptions. Independence of observations is treated as the most critical: if observations are linked (for instance, if one person’s outcome influences another’s), p-values can become misleadingly small, increasing the risk of false “significant” findings. The variable should be measured on an interval or ratio (numerical) scale. Normality is also required for fully reliable inference, but the session emphasizes that the t test is fairly robust to mild departures—especially with moderate or large samples.

An SPSS walkthrough grounds these ideas in a concrete example. A business school claims its graduates earn an average of 750,000 rupees per year. A sample of 30 graduates is collected, and the null hypothesis is set as “the population mean equals 750,000.” Before running the test, SPSS is used to check normality via skewness and kurtosis from descriptive statistics; the reported skewness is -0.263 and kurtosis is -0.744, both within commonly cited acceptable ranges. Then SPSS runs the one-sample test under “Analyze → Compare Means → One-Sample T Test,” using 750,000 as the test value.

The output shows a sample mean of 691.584 (with n=30) and a two-tailed p-value reported as 0 (with t = -6.184 and df = 29). With a 5% significance level, p < 0.05 leads to rejection of the null hypothesis. The conclusion is straightforward: the graduates’ average salary is significantly different from the advertised 750,000, and because the sample mean is lower, the claim does not hold.