To analyze the data from the matched pairs design and compare the proportions, you can use one-sample procedures for proportions. Let's break down the steps:
Step 1: Define the null and alternative hypotheses.
- Null hypothesis (H0): There is no difference in preference between Times New Roman and Gigi fonts for web use.
- Alternative hypothesis (Ha): There is a difference in preference between Times New Roman and Gigi fonts for web use.
Step 2: Conduct the statistical analysis.
- You have a sample size of 25 volunteers who read the same text in both fonts.
- Out of the 25 subjects, 17 preferred Times New Roman for web use, while 20 preferred Gigi.
- To analyze the data, you can use a one-sample proportion test. This test compares the observed proportion (p) to a hypothesized proportion (p0) specified in the null hypothesis.
Step 3: Calculate the test statistic.
- Calculate the observed proportion (p) of subjects who preferred Times New Roman: p = 17/25 = 0.68.
- Calculate the hypothesized proportion (p0) specified in the null hypothesis (50% since there is no difference assumed): p0 = 0.50.
- Calculate the standard error (SE) of the proportion: SE = sqrt(p0 * (1 - p0) / n) = sqrt(0.50 * 0.50 / 25) = 0.10.
- Calculate the test statistic (z-score): z = (p - p0) / SE = (0.68 - 0.50) / 0.10 = 1.8.
Step 4: Determine the critical value and p-value.
- The critical value for a two-sided test at a significance level of 0.05 is approximately ±1.96 (from a standard normal distribution table).
- Calculate the p-value associated with the observed test statistic using a standard normal distribution table or statistical software. The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.
Step 5: Make a conclusion.
- If the observed test statistic falls within the critical region (outside the range defined by the critical values), the null hypothesis is rejected in favor of the alternative hypothesis.
- Alternatively, if the p-value is less than the chosen significance level (usually 0.05), the null hypothesis is rejected.
Note: The analysis for the preference of Gigi font can be done using the same steps, replacing the proportions and calculating another z-score.
Keep in mind that it's essential to use appropriate statistical software or consult a statistician to perform these calculations accurately.