Compare The Long-Term Psychological Effects Of Different Dye ✓ Solved

Compare the long-term psychological effects of different diets and conduct related statistical analyses

Researchers aimed to compare the psychological effects of two energy-restricted diets — a high-carbohydrate, low-fat (LF) diet and a high-fat, low-carbohydrate (LC) diet — on psychometric assessments over a one-year period. The study involved 106 overweight and obese participants, randomly assigned to these diets. At 52 weeks, data was available for 65 participants (32 LC and 33 LF). Mood was measured using the total mood disturbance score (TMDS), where lower scores indicate a better mood. The summarized data were: for the LC group, n=32, mean=47.3, standard deviation=28.3; for the LF group, n=33, mean=19.3, standard deviation=25.8. The objectives include testing whether there is a significant difference in TMDS scores between the two diet groups, using a significance level of 0.05.

Sample Paper For Above instruction

This paper examines the long-term psychological impacts of two different dieting strategies — high-carbohydrate, low-fat (LF) and high-fat, low-carbohydrate (LC) — by analyzing the total mood disturbance scores (TMDS) of participants after 52 weeks. The statistical analysis involves hypothesis testing to determine whether the observed differences in TMDS scores are statistically significant, reflecting a meaningful difference in psychological well-being between the two diet groups.

Introduction

Diet plays a critical role not only in physical health but also in psychological well-being. The comparative effects of different macronutrient-focused diets on mental health have garnered considerable attention in nutritional and psychological research. This study explores whether a high-fat, low-carbohydrate diet yields different long-term effects on mood compared to a high-carbohydrate, low-fat diet among overweight and obese individuals. The primary outcome measure is the total mood disturbance score (TMDS), where a lower score indicates a more positive mood.

Methodology

The participants were randomly assigned to either the LC or LF diet. Post 52 weeks, the mood scores were summarized as follows: the LC group had a mean TMDS of 47.3 with a standard deviation of 28.3 based on 32 individuals, and the LF group had a mean of 19.3 with a standard deviation of 25.8 based on 33 individuals. The hypothesis test compares the population means of the TMDS scores in both groups. The null hypothesis (H0) states that there is no difference in the mean TMDS scores between the two diets (μ_LC = μ_LF), while the alternative hypothesis (H1) suggests that the means are different (μ_LC ≠ μ_LF).

Results and Analysis

First, we perform an independent samples t-test assuming unequal variances, also known as Welch's t-test. The test statistic is calculated as:

\[ t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]

where:

  • \(\bar{X}_1 = 47.3\), \(s_1=28.3\), \(n_1=32\) (LC group)
  • \(\bar{X}_2=19.3\), \(s_2=25.8\), \(n_2=33\) (LF group)

Calculating the standard error:

\[ SE = \sqrt{\frac{28.3^2}{32} + \frac{25.8^2}{33}} \approx \sqrt{\frac{802.89}{32} + \frac{665.64}{33}} \approx \sqrt{25.09 + 20.17} \approx \sqrt{45.26} \approx 6.73 \]

Thus, the t-statistic:

\[ t = \frac{47.3 - 19.3}{6.73} \approx \frac{28}{6.73} \approx 4.16 \]

Next, the degrees of freedom (df) are estimated using the Welch-Satterthwaite equation:

\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 -1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 -1}} \]

Plugging in the values yields approximately df ≈ 55.

Using a t-distribution table or software, the p-value associated with t=4.16 and df≈55 is less than 0.001. Since p

Discussion

The analysis provides strong evidence that the type of diet influences psychological well-being after one year, with the high-fat, low-carb diet group exhibiting higher (worse) mood disturbance scores. This suggests that diet composition can significantly impact mental health, emphasizing the importance of considering psychological effects alongside physical health outcomes in dietary interventions.

Conclusion

Based on the results, we conclude that there is a significant difference in total mood disturbance scores between participants on the LC and LF diets after 52 weeks. The high-fat, low-carb diet appears to be associated with a less favorable psychological profile, as reflected in higher TMDS scores. Future research should further explore long-term psychological impacts and potential mechanisms underlying these differences.

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