A Study Examined Whether Adding A Fragrance To A Window Clea

A Study Examined Whether Adding A Fragrance To A Window Cleaner Led

A study examined whether adding a fragrance to a window cleaner influenced people's perceptions of its cleaning effectiveness. The study involved two groups: one using scented cleaner and the other using unscented cleaner, with 12 subjects in each group. The mean effectiveness rating for the scented cleaner was 7.42, while for the unscented cleaner, it was 6.00. The standard deviation across all subjects was 1.369. A t-test indicated that the scented cleaner was rated significantly more effective (p

Additionally, another study compared the amount of study time between male and female college students, with 10 males and 10 females. The mean study time was 11.1 hours/week for males and 10.9 hours/week for females, with a pooled standard deviation of 2.81. The t-test revealed no significant difference in study time (p > .10).

There are also questions regarding statistical power, Type 2 error, and effect size calculations based on given parameters and a table for effect sizes at a significance level of .05 in a two-sample independent t-test context.

Paper For Above instruction

Introduction

Understanding the impact of scent on consumer perception and the significance of effect sizes in research are critical areas in psychological and behavioral studies. This paper explores two research studies—one examining the influence of fragrance on cleaning perceptions and another investigating gender differences in study habits—and discusses concepts of statistical power, Type 2 errors, and effect size calculations. The analysis emphasizes the practical implications of the research findings and the importance of effect sizes and power analysis in designing robust experiments.

Analysis of the Fragrance and Cleaning Effectiveness Study

The first study investigates whether adding a fragrance to a window cleaner affects individuals' perceptions of its efficacy. With mean ratings of 7.42 for the scented and 6.00 for the unscented cleaner, and a pooled standard deviation of 1.369, the effect size measurement provides insight into the practical significance of these findings. Calculating Cohen’s d, a standardized effect size measure, involves the difference in means divided by the pooled standard deviation:

Cohen's d = (Mean₁ - Mean₂) / SDpooled

Substituting the values:

Cohen's d = (7.42 - 6.00) / 1.369 ≈ 1.42 / 1.369 ≈ 1.037

This value suggests a large effect size according to Cohen’s conventions (Cohen, 1988), indicating a practically significant difference in perceived cleaning efficacy between scented and unscented cleaners.

Interpreting this effect size, it is evident that the addition of fragrance not only influences consumer perception statistically but also exerts a large practical impact. The difference being over one standard deviation signifies that consumers perceive the scented cleaner as substantially more effective. Such insights have implications for product marketing, suggesting that scent plays a vital role in consumer judgments beyond objective cleaning performance.

Analysis of the Gender and Study Time Study

The second study assesses whether gender influences the amount of time college students dedicate to studying. With means of 11.1 hours/week for males and 10.9 hours/week for females, and a pooled standard deviation of 2.81, the effect size calculation again employs Cohen’s d:

Cohen's d = (11.1 - 10.9) / 2.81 ≈ 0.2 / 2.81 ≈ 0.071

This effect size is very small, falling well below Cohen’s threshold for a small effect (.20), indicating that the difference in study time between males and females is practically negligible.

The absence of statistical significance (p > .10) aligns with this small effect size, reinforcing the conclusion that gender does not meaningfully influence study habits in this context. From a practical standpoint, efforts to tailor study programs based on gender differences in study time may not be justified given the minimal effect size observed.

Power, Type 2 Error, and Effect Size Calculations

Statistical power reflects the probability of correctly detecting a true effect, while Type 2 error (β) indicates the probability of failing to detect such an effect when it exists. When power is 84%, the Type 2 error is simply calculated as:

Type 2 Error (β) = 1 - Power = 1 - 0.84 = 0.16 or 16%

Similarly, if the Type 2 error is 12%, the power is:

Power = 1 - 0.12 = 0.88 or 88%

These calculations guide researchers in understanding the likelihood of Type 2 errors and setting appropriate sample sizes during study design.

Sample Size and Effect Size in Study Design

Using the provided table and targeting a power of .80 with an expected effect size of Cohen’s d = .80 (large effect), the required sample size per group can be estimated from typical power tables or software. For a large effect (d = .80) and power of .80, approximately 26 subjects per group are needed, according to G*Power calculations (Faul et al., 2007). This number ensures a high probability of detecting a true large effect.

If a researcher can recruit 65 subjects per group, then the study's power would increase. To determine the minimum Cohen’s d necessary for this sample size to maintain .80 power, interpolation from the table suggests that with 65 subjects per group, an effect size slightly below large (around .70) could achieve the desired power.

For smaller effect sizes, such as .65, the required sample size increases to maintain .80 power; approximately 34 participants per group are necessary (see calculations based on effect size and power considerations). Conversely, with only 25 subjects per group, the effect size needed for .80 power would be just above medium, around .70, indicating that smaller sample sizes require larger effects to reliably detect differences (Cohen, 1988).

Conclusion

Assessing the effect of scent on perceived cleaning effectiveness reveals a large, practically significant effect size, emphasizing scent's influence on consumer perceptions. Conversely, the minimal difference in study time between genders underscores the importance of effect size over mere statistical significance in interpreting practical relevance. Power analysis and effect size calculations are indispensable tools in research design, ensuring studies are adequately powered to detect true effects. Balancing sample sizes and anticipated effect sizes allows researchers to optimize resources and improve the robustness of their findings, ultimately contributing to more accurate and meaningful scientific conclusions.

References

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