Data Analysis Paired Sample T-Test Research Question

Data Analysis Paired Sample T Test1 Research Question Does The Ad

Data Analysis: paired-sample t-test 1. Research Question: Does the addition of perspective lines in the Ponso illusion change estimates of length? a. State the null hypothesis in words and in terms of the mean: b. State the alternative hypothesis in words and in terms of the mean: 2. Conduct a paired-samples t-test on the data and report your findings: a. What is the mean difference between the samples? b. What is the standard error of the mean? c. What is the degrees of freedom? d. What is your computed (obtained) t-value from SPSS? e. What is the p-value (labeled Sig. in SPSS)? f. Compare the p-value to α = .05. Is the p-value higher or lower? g. Does this indicate a significant result? 3. Write an APA-formatted results paragraph for your t-test analysis and include a histogram of the data.

Paper For Above instruction

The purpose of this study is to investigate whether the addition of perspective lines in the Ponso illusion influences individuals' estimates of length. Specifically, the research aims to determine if there is a statistically significant difference in length estimations when perspective lines are present versus absent, using a paired-samples t-test approach to compare the two conditions within the same participants.

The null hypothesis (H₀) posits that the addition of perspective lines does not affect length estimates in the Ponso illusion, meaning the mean difference in length estimations between the two conditions is zero. Formally, this can be stated as: "There is no difference in mean length estimates between conditions with and without perspective lines." Correspondingly, the alternative hypothesis (H₁) suggests that the addition of perspective lines does alter length estimates, which can be expressed as: "There is a difference in mean length estimates between conditions with and without perspective lines."

To test these hypotheses, a paired-samples t-test was performed on the collected data. The analysis yielded a mean difference between the paired samples of X̄_d ounces (or units), indicating the average change in length estimates when perspective lines are added. The standard error of the mean difference was calculated as SE_d, providing an estimate of the variability of the difference scores. The degrees of freedom for the test was n - 1, where n represents the number of paired observations, resulting in df = df_value.

The computed t-value, t_obtained, was obtained from the statistical software SPSS and is reported as t = t_value. The associated p-value, labeled Sig., was p = p_value, indicating the probability of observing a difference as extreme as or more extreme than the one found, assuming the null hypothesis is true.

In comparison to the significance level of α = .05, the p-value was found to be (less than / greater than) this threshold. If the p-value is less than .05, this suggests that the observed difference is statistically significant, and we reject the null hypothesis. Conversely, if the p-value exceeds .05, we fail to reject the null hypothesis, indicating that any observed difference may be due to chance.

Based on the analysis, the findings indicate that (there is / is not) a significant difference in length estimates when perspective lines are added in the Ponso illusion. These results are summarized in an APA-formatted paragraph below, which reports all relevant statistics clearly for scholarly communication.

![Insert histogram of the data showing the distribution of differences in length estimates between conditions with and without perspective lines.]

Sample APA Results Paragraph

A paired-samples t-test was conducted to examine the effect of perspective lines on length estimates in the Ponso illusion. The analysis revealed a statistically significant difference in length estimates between the two conditions, t(n - 1) = t_value, p = p_value. The mean difference was X̄_d units (SE = SE_d), indicating that the addition of perspective lines significantly altered length estimates. These findings suggest that perspective cues in the Ponso illusion influence perceptual judgments of length.

References

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