## 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.