Task 1: Statistical Analysis of Film Responses
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.
|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|
|5% Trimmed Mean||37.44|
|A documentary about notebooks||Mean||13.25||1.594|
|95% Confidence Interval for Mean||Lower Bound||9.91|
|5% Trimmed Mean||13.22|
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.
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
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.