Psy 315 Phoenix University: Questions For The Chapter

Psy 315 Phoenix Universityhere Are The Questions For Chapter 9s Food

These questions explore foundational concepts in experimental research design and statistical analysis within the context of Chapter 9's focus on food-related studies. Topics include the distinction between between-subjects and within-subjects designs, detailed examination of the two-independent samples t-test, calculations of effect size, degrees of freedom, and interpretation of test results. The questions provide a comprehensive review of the statistical methodologies used when comparing groups in psychological research, emphasizing both theoretical understanding and practical application.

Paper For Above instruction

Experimental research in psychology often involves comparing groups to understand the effects of different variables, and the two-independent samples t-test is a fundamental tool for such comparisons. This paper discusses key concepts about research designs, the assumptions underlying statistical tests, calculations involved, and interpretations necessary for analyzing data and drawing valid conclusions.

Between-Subjects and Within-Subjects Designs

A between-subjects design involves different participants being assigned to each condition or group in a study. This means that each participant experiences only one condition, and comparisons are made between different groups. For example, in a study examining the effect of a dietary intervention on weight loss, one group might receive the intervention while another does not.

In contrast, a within-subjects design involves the same participants experiencing all conditions or treatments. This design controls for individual differences because each participant serves as their own control. An example would be measuring the same individuals’ responses to different types of foods to see how preference varies within subjects.

The key distinction lies in whether the same participants are exposed to multiple conditions (within-subjects) or whether different participants are assigned to different groups (between-subjects). The choice depends on research goals, practical considerations, and statistical properties.

Two-Independent Sample t-Test: Definition and Assumptions

The two-independent sample t-test compares the means of two independent groups to determine whether they differ statistically significantly. It assesses whether the observed difference between the sample means reflects a true difference in the population means or is due to sampling variability.

The assumptions of this test include:

• Independence of observations: The data collected from different groups should have no overlap.
• Normality: The distribution of the data within each group should be approximately normal, especially for small sample sizes.
• Homogeneity of variances: The variances in each group should be roughly equal, which can be tested using Levene's test or similar procedures.

Critical Value for a Two-Tailed Test at α = .05

For a study measuring the difference between men and women with samples of 13 and 15 respectively, the degrees of freedom (df) are calculated as df = (n1 - 1) + (n2 - 1) = 12 + 14 = 26. Consulting a t-distribution table or using statistical software, the critical t-value for a two-tailed test at α = .05 with df = 26 is approximately ±2.056. This means that if the test statistic exceeds ±2.056 in magnitude, the difference is statistically significant at the 5% significance level.

Denominator for Cohen's d in Two-Independent Sample t-Test

The denominator in Cohen's d for two independent means is the pooled standard deviation, which combines the variability from both groups and accounts for unequal sample sizes. It is calculated as:

spooled = √[( (n1 - 1) s1² + (n2 - 1) s2² ) / (n1 + n2 - 2)]

This pooled standard deviation provides a measure of the common variability used in effect size calculations.

Estimating Cohen's d with Different Standard Deviations

The formula for Cohen's d is:

d = (M1 - M2) / spooled

Given a mean difference of 4, the effect size estimates are as follows:

• (a) Standard deviation = 4: d = 4 / 4 = 1.0
• (b) Standard deviation = 8: d = 4 / 8 = 0.5
• (c) Standard deviation = 16: d = 4 / 16 = 0.25
• (d) Standard deviation = 40: d = 4 / 40 = 0.1

This illustrates how larger variability reduces the magnitude of the effect size.

Calculating Degrees of Freedom, Variance, and Standard Deviation

The degrees of freedom for a two-independent sample t-test are typically calculated as df = n1 + n2 - 2; in this case, 13 + 15 - 2 = 26. The pooled sample variance is computed as:

s²_pooled = [(n1 - 1) s1² + (n2 - 1) s2²] / (n1 + n2 - 2)

And the pooled sample standard deviation is the square root of this variance: the square root of the pooled variance.

Participants in Independent Samples

In an independent sample, different participants are observed in each group. There is no overlap; each group consists of unique individuals, which is important for ensuring the assumption of independence.

Measures of Effect Size

Three common measures used to estimate effect size in the context of the two-independent-sample t-test include:

1. Cohen's d
2. Hedges' g
3. Glass's delta

These measures quantify the magnitude of differences between groups, providing context beyond mere statistical significance.

Steps to Compute an Effect Size Estimation Formula

The typical steps are:

1. Calculate the mean difference (M1 - M2).
2. Calculate the pooled standard deviation.
3. Divide the mean difference by the pooled standard deviation to arrive at Cohen's d.

Choosing the Appropriate t-Test

(a) Comparing attitudes about morality among men and women involves two groups, making a two-independent sample t-test appropriate.

(b) Testing if night-shift workers sleep 8 hours requires a one-sample t-test, as it compares the sample mean to a known value.

(c) Measuring differences in brain activity among rats on different reward schedules involves two independent groups, again requiring a two-independent sample t-test.

Effects on the Test Statistic

(a) Increasing the total sample size tends to increase the test statistic's power, potentially increasing its value if differences exist.

(b) Reducing the significance level from .05 to .01 makes the test more conservative, which can decrease the likelihood of finding significance, effectively lowering the critical value but not directly affecting the test statistic per se.

(c) Doubling the pooled sample variance inflates the denominator, which decreases the t-value, making it less likely to reach significance.

When is an Independent t-Test Appropriate?

The independent t-test is appropriate for comparing the means of two independent groups when the data meet the assumptions of independence, normality, and homogeneity of variances. It helps establish whether differences between group means are statistically significant.

Interpreting the t-Value

The t-value quantifies the standardized difference between the group means relative to variability. A larger absolute t-value indicates a greater likelihood that the observed difference is genuine rather than due to chance. A p-value associated with t determines significance.

For example, t(28) = -0.16, p > .05 (not significant), indicates that the observed difference is very small, and there is no evidence to suggest a real difference between the groups.

Conclusion

Understanding the proper use, assumptions, and interpretation of the two-independent sample t-test is crucial for psychological research. Correct application ensures valid conclusions about differences between groups, which underpins scientific knowledge development in the field of psychology and related disciplines.

References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge Academic.
• Geiser, C. (2013). Data analysis with SPSS: An introduction for students in the social sciences. Routledge.
• Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.
• Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the behavioral sciences. Cengage Learning.
• Kirk, R. E. (2013). Experimental design: Procedures for the behavioral sciences. Sage Publications.
• Laerd Statistics. (2018). Independent samples t-test using SPSS Statistics. Retrieved from https://statistics.laerd.com/
• Leech, N. L., Barret, K. C., & Morgan, G. A. (2015). SPSS for intermediate statistics. Routledge.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson Education.
• Wilson, R. J. (2010). Using SPSS: An interactive handbook. Routledge.
• Field, A., Miles, J., & Field, Z. (2012). Discovering statistics using R. Sage.