RPUBS

INTRODUCTION

THE EVOLUTION OF THE WORLD OF ENTERTAINMENT

Before the film industry was revolutionized with the proliferation of video-on-demand and online streaming services, 3d/4d films, and popularity of blockbuster comic book movies, the cinematic universe was influenced by the significant developments which happened in the earlier decades.

INTRODUCTION

DEVELOPMENTS THAT DEFINED 1990s AND 2000s

PROBLEM STATEMENT

Both decades were known for its respective iconic, award-winning, and top-grossing pictures.

METHODOLOGY

DATA SOURCE

• Information courtesy of IMDb http://www.imdb.com. Used with permission.
  • For compliance, no alterations or republishing were made. Only the results from the statistical tests were shown.
  • Analysis was limited to the public data provided.

METHODOLOGY

SAMPLING

• Only titles with more than 30 votes were selected to ensure a more accurate representation.
• Total sample size \(n = 42,996\)

STATISTICAL TESTS

An independent two-sample t-test (at 95% CI) was performed upon meeting the following conditions:

1. Scanning and handling of outliers using Tukey’s method
2. Testing the assumption of normality using skewness and kurtosis tests
3. Testing the homogeneity of variance using Levene’s test

RESULTS

CONDITION 1: TUKEY’S METHOD OF OUTLIER DETECTION

RESULTS

SUMMARY STATISTICS

RESULTS

CONDITION 2: TESTING THE ASSUMPTION OF NORMALITY

• Most of the quantile points in the 1990s and 2000s data fall within the theoretical normal line which indicated that both are normally distributed.

RESULTS

CONDITION 2: TESTING THE ASSUMPTION OF NORMALITY

• This was further evidenced by the skewness and kurtosis test results.
  • Skewness statistic: Both decades are within +/-2 which proved a symmetric distribution.
  • Kurtosis statistic: Both decades are within +/-2 which mirrored the tail thickness of a normal distribution.
• This means that an independent t-test can be applied effectively.

skewness(Decade_1990$averageRating)

## [1] -0.3432102

kurtosis(Decade_1990$averageRating)

## [1] -0.3270806

skewness(Decade_2000$averageRating)

## [1] -0.4261925

kurtosis(Decade_2000$averageRating)

## [1] -0.2611371

RESULTS

CONDITION 3: HOMOGENEITY OF VARIANCE (LEVENE’S TEST)

• The p-value for the average user rating between the 1990s and 2000s is \(\ p < 0.001\). In comparison to the standard significance level of \(\alpha (p < 0.05)\), the result is statistically significant.
• Therefore, equal variance cannot be assumed for this study.

leveneTest(IMDB5$averageRating ~ IMDB5$Decade, data = IMDB5)

## Levene's Test for Homogeneity of Variance (center = median)
##          Df F value    Pr(>F)    
## group     1  13.584 0.0002284 ***
##       42994                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

HYPOTHESIS TESTING

AN INDEPENDENT TWO-SAMPLE t-TEST ASSUMING UNEQUAL VARIANCE

\[H_0: \mu_1 - \mu_2 = 0\]

\[H_A: \mu_1 - \mu_2 \ne 0\]

where \(\mu_1\) and \(\mu_2\) represent the population means of the two groups: 1990s and 2000s respectively.

DECISION RULES

• Fail to reject H₀ if:

  • t-statistic does not lay within the critical region
  • \(\alpha (p > 0.05)\)
  • H₀ is captured within the confidence interval

• Otherwise, reject H₀.

HYPOTHESIS TESTING

AN INDEPENDENT TWO-SAMPLE t-TEST ASSUMING UNEQUAL VARIANCE

Two-tailed test’s significance level was \(\alpha = 0.05\). Welch t-test was applied following the unequal variance assumption.

t.test(Decade_1990$averageRating, Decade_2000$averageRating, var.equal = FALSE, alternative = "two.sided")

## 
##  Welch Two Sample t-test
## 
## data:  Decade_1990$averageRating and Decade_2000$averageRating
## t = -2.6229, df = 31337, p-value = 0.008722
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.05464682 -0.00790437
## sample estimates:
## mean of x mean of y 
##  6.030050  6.061325

CRITICAL VALUE THRESHOLD: +/- 1.96

qt(p = 0.05/2, df = 14882   + 28114 - 2, lower.tail = FALSE)

## [1] 1.960019

DISCUSSION

INTERPRETATION OF THE RESULTS

A two-sample t-test was performed to check for a significant difference between the mean average user rating of the movies in the 1990s and 2000s.

• The Levene’s test of homogeneity of variance indicated that equal variance cannot be assumed.
  • \(p < 0.001\) is less than standard significance level of \(\alpha (p < 0.05)\)
• The results of the two-sample t-test assuming unequal variance was statistically significant.
  • \(t(df = 31,337) = -2.62\) t-statistic lays within the critical region
  • \(p = 0.01\) is less than standard significance level of \(\alpha (p < 0.05)\)
  • H₀ is not captured within the 95% CI for the difference in means [-0.05 -0.01]

DISCUSSION

INTERPRETATION OF THE RESULTS

The central tendencies of both decades lie within the rating of 6.0 to 6.2, with majority of the data ranging between 4.5 to 7.5. However, note that the distinguishable variations came from the distribution of higher ratings in 2000s.

CONCLUSION

SUMMARY

The results of the investigation suggest that there is a statistically significant difference between the average user rating of the movies in the 1990s and 2000s, t(df = 31,337) = −2.62, p = 0.01, 95% [-0.05 -0.01].

Movies in the 2000s have significantly higher average user ratings than the movies in the 1990s.

• Examples of the highly-rated movies on IMDb:

RECOMMENDATIONS

In spite of the significant developments observed in the 1990s and 2000s, statistical tests applied, and substantial sample size, there are limitations associated with claiming 2000s as “The Best Decade for Movies”.

A more stringent criteria, sample, and/or advanced statistical test would be the best approach to reduce further variabilities and maximize the outcome of this research.

REFERENCES