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Exploring Statistical Methods in Film Analysis: Assessing Normality Assumptions and Addressing Data Transformations

In this statistical exploration, we delve into the intricacies of psychological arousal analysis during film viewing. Through rigorous testing and descriptive statistics, we evaluate the normality assumptions of viewer responses to films like "The Notebook" and a documentary about notebooks. Additionally, we tackle the challenge of positively skewed data, opting for a data transformation approach to enhance the reliability of our statistical inferences.

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Task 1: Statistical Analysis of Film Responses

Problem Description:

The statistical analysis assignment involves conducting a statistical analysis of psychological arousal during the film viewing experience, comparing two films, "The Notebook" and a documentary about notebooks. The focus is on validating assumptions and presenting descriptive statistics, normality tests, Q-Q plots, and ANOVA results.

Descriptive Statistics:

Descriptive

Name of Film Statistic Std. Error
Psychological Arousal During the Film The notebook Mean 37.30 1.613
95% Confidence Interval for Mean Lower Bound 33.92
Upper Bound 40.68
5% Trimmed Mean 37.44
Median 38.00
Variance 52.011
Std. Deviation 7.212
Minimum 23
Maximum 49
Range 26
Interquartile Range 9
Skewness -.302 .512
Kurtosis -.281 .992
A documentary about notebooks Mean 13.25 1.594
95% Confidence Interval for Mean Lower Bound 9.91
Upper Bound 16.59
5% Trimmed Mean 13.22
Median 12.50
Variance 50.829
Std. Deviation 7.129
Minimum 2
Maximum 25
Range 23
Interquartile Range 11
Skewness .040 .512
Kurtosis -1.024 .992

Table 1: Descriptive statistics and its results

Psychological Arousal During "The Notebook"

  • Mean: 37.30
  • 95% Confidence Interval for Mean: (33.92, 40.68)
  • 5% Trimmed Mean: 37.44
  • Median: 38.00
  • Variance: 52.011
  • Std. Deviation: 7.212
  • Minimum: 23, Maximum: 49
  • Range: 26, Interquartile Range: 9
  • Skewness: -0.302, Kurtosis: -0.281

Psychological Arousal During "Documentary about Notebooks"

  • Mean: 13.25
  • 95% Confidence Interval for Mean: (9.91, 16.59)
  • 5% Trimmed Mean: 13.22
  • Median: 12.50
  • Variance: 50.829
  • Std. Deviation: 7.129
  • Minimum: 2, Maximum: 25
  • Range: 23, Interquartile Range: 11
  • Skewness: 0.040, Kurtosis: -1.024

Normality Tests and Q-Q Plots:

  • The Z-scores for skewness and kurtosis are calculated for both films.
  • Q-Q plots suggest a somewhat normal distribution with a few data points deviating from expected values.

Tests of Normality:

Kolmogorov-Smirnova Test and Shapiro-Wilk Test

  • The Notebook:

K-S Statistic: 0.125 (df: 20, Sig.: 0.200*)

Shapiro-Wilk Statistic: 0.968 (df: 20, Sig.: 0.722)

  • Documentary about Notebooks:

K-S Statistic: 0.097 (df: 20, Sig.: 0.200*)

Shapiro-Wilk Statistic: 0.960 (df: 20, Sig.: 0.552)

(*Note: Significance corrected using Lilliefors correction)

  • The K-S test indicates a rejection of the null hypothesis, suggesting non-normality.

ANOVA Results:

Biological Sex of Participant and Psychological Arousal

  • Between Groups: Sum of Squares = 0.000, df = 1, Mean Square = 0.000, F = 0.000, Sig. = 1.000
  • Within Groups: Sum of Squares = 10.000, df = 38, Mean Square = 0.263
  • Total: Sum of Squares = 10.000, df = 39

The F value (< 0.05) indicates a violation of the assumption in the data.

Task 2: Data Transformation for Positively Skewed Distribution

Problem Description:

This task involves dealing with a positively skewed distribution in the dataset. The options considered for transformation are log, square root, and reciprocal. The choice is made based on the suitability of non-normally distributed data.

Chosen Transformation: Reciprocal transformation is selected as it is known to be effective for non-normally distributed data.