Introduction
Statistical analysis is appropriate when the quality of decisions has broad practical potential, and their consequences can affect the industry. However, statistics is also applicable when the author intends to reduce bias and systematic error, and the conclusions should be objective and unbiased to the greatest extent possible.
Additionally, conducting statistical analysis through an integrated approach, which involves performing not only descriptive statistics but also several multivariate inference tests, ensures that no potential relationships or outcomes in the distributions are ignored. Thus, the quality of the analysis performed increases. Thus, pursuing the described strategies, the present work continues to study the Spotify Songs dataset. This dataset contains more than 30,000 rows of unique songs from the Spotify streaming service, including author, genre, playlist membership, track duration, and output characteristics (popularity, danceability, and tempo).
Variable Distribution
Two significant analysis phases had already been conducted, each including differential tasks. During the first milestone of the statistical investigation of the dataset, the distributions of the variables were examined in general terms, with the results of descriptive statistics interpreted according to the nature of the variables. The results included identifying the most popular genre playlist, listing the top 10 musical artists with the most songs in the sample, and performing a correlation analysis of continuous variables to assess potential relationships. The functional essence of this step was to gain initial insights into the dataset and to understand the key trends in the distributions (Mishra et al., 2019).
Research Questions, One-Way ANOVA and One-Sample T-Test
The second stage of the statistical study involved a more in-depth analysis, including formulating research questions and hypotheses, and conducting a one-way ANOVA and a one-sample t-test (Amrhein et al., 2019). In other words, the second milestone focused on a comparative analysis to test differences in track popularity characteristics between the six genre playlists (ANOVA) and the statistical significance of differences in the sample mean tempo of songs in the EDM playlist from the target of 120.88 bpm (one-sample t-test). The results of the second stage showed significant differences in popularity across almost all six genre playlists, with the most popular tracks being pop and Latin American songs. In addition, the EDM playlist resulted in higher heart rates in listeners than the target. The functional essence of the second phase of the statistical study thus lay in investigating differences in the dataset’s composition across group affiliations.
Regression Analysis
Finally, it was decided to proceed to the following statistical analysis stage, which involved more profound work with the data. The present stage of analysis involved conducting regression analysis on the one hand and an additional ANOVA test on the other. First, the regression analysis aimed to investigate the effect of a potential predictor on the dependent variable, with two purposes: to explore causal relationships between continuous numerical variables and to develop a predictive model (Montgomery et al., 2021).
Second, an additional one-way ANOVA was conducted to create categorical groups based on the music track tempo variable and then to assess differences in mean popularity scores between groups (Yu et al., 2022). The semantic essence of this extension was to push the boundaries of statistical research and to build an even deeper understanding of the patterns in the data and how the findings can be used to construct practical recommendations for performers. Thus, this report aims to conduct and summarize new statistical analyses of the Spotify Songs dataset and to offer data-driven recommendations for increasing the expected popularity of musicians’ published tracks.
Research Questions and Hypotheses
As with any other step in inferential analysis, the regression test and the one-way ANOVA had to be based on clear, understandable research questions from which the research hypotheses are derived.
Thus, the two research questions of this phase of analysis included the following:
- How does the track duration index affect the level of track popularity?
- Are there differences in the average popularity rates of tracks formed between different groups according to their tempo criterion?
To answer these questions, four hypotheses were constructed, two for each:
- ▪ H10: The duration of tracks does not affect their popularity (B = 0).
- ▪ H11: The length of tracks affects their popularity (B ≠ 0).
- ▪ H21: There were no differences in the mean popularity of the tracks between the groups formed according to the tempo criterion.
- ▪ H22: There was at least one pairwise difference in the mean track popularity scores between the groups formed according to the tempo criterion.
As noted, all hypotheses were non-directional, so two-tailed tests were used. An alpha significance level of.05 was chosen to test the significance of the effects and differences found. In other words, if the resulting p-value was above 0.05, it indicated that the hypothesis being tested was not statistically significant.
Results of Hypothesis Testing
Regression Analysis
The regression analysis evaluated the effect of track duration (independent variable, predictor) on track popularity (dependent variable, response). Since only one predictor was studied, a simple linear regression model was used (Montgomery et al., 2021). The results of the regression analysis indicate a statistically significant influence model (F(1, 32831) = 692.1, p <.000), as shown in Appendix B. In other words, this model could be used to critically discuss the relationship between track duration and popularity.
The coefficient of determination for the model was 0.02064, indicating, however, a relatively low proportion of variance explained: duration accounted for only 2.064% of the variance in track popularity scores. This indirectly indicated that popularity is not a strict function of duration, and that many other factors likely affect expected popularity. However, the predictor (track duration) was statistically significant (B = -3.5997, p <.000). This shows that for every one-minute increase in track length, the popularity score was inclined to decrease by 3.5997 units out of 100. In other words, a track lasting 27.78 minutes was rated as having predictably zero popularity.
Critically evaluating the regression model constructed, [y = -3.5997x + 0.1368], it should be clarified that the y-intercept implies a non-zero popularity for a track at zero duration. This makes no real sense, since there is no song with a zero track duration; thus, it is an analysis error. In other words, the results of the regression test show that, on the one hand, a reduction in track duration is a predictor of popularity growth. On the other hand, the detected effect should be used with caution, as the model is not very reliable.
ANOVA Test
ANOVA was conducted to test for differences across groups in track tempo (independent variable) and popularity scores (dependent variable). Since the estimated tempo was a continuous variable, the primary transformation was to a categorical variable with six levels: ‘low tempo,’ ‘moderate tempo,’ ‘medium tempo,’ ‘high tempo,’ ‘very high tempo,’ and ‘extreme tempo.’ The categorization of a track into a particular group was based on the tempo index: the first group included tracks with a tempo from 0 to 40 bpm, the second from 41 to 80 bpm, and so on. It was shown that each of the above groups contained the following numbers of inclusions: 4, 1338, 14038, 14247, 3063, and 143, respectively.
On the one hand, this indicated a bias towards a normal distribution, with central values having peak shapes and marginal values minimized. On the other hand, the low number of observations in the left margin indicated a need to rethink the model, as the four data points were insufficient for a reliable ANOVA. After changing the criterion and reducing the groups to 4, the following groups were obtained: “low tempo” (n = 26), “medium-low tempo” (n = 15354), “medium-high tempo” (n = 16572), and “high tempo” (n = 881), which indicated that an ANOVA was possible.
First, the results confirmed the presence of statistically significant effects (F(3, 32829) = 37.79, p <.000) as shown in Appendix C. This indicated differences among the four groups. To identify the locations of these differences, a Tukey post hoc test was used to determine whether differences existed only between some groups. In particular, the “medium-high tempo” and “medium-low tempo” groups were statistically significantly different from each other, as were “high tempo” and “medium-high tempo.” The popularity of “medium-low tempo” and “high tempo” was significantly higher than that of “medium-high tempo”.
Conclusion
The deeper level statistical analysis aimed to test the factors affecting the popularity of the tracks. Significant effects and differences were found using regression analysis and one-way ANOVA. On the one hand, it was shown that longer track duration is associated with lower popularity, suggesting that artists could consider strategies to shorten their tracks. However, this relationship shows substantial unexplained variance, indicating the need for a more detailed study.
On the other hand, significant differences in track popularity were observed among the top three bpm tempo groups. This may indicate the need to keep the tempo of tracks at 61-120 bpm and 181-240 bpm to increase their popularity. These findings can serve as sound recommendations for authors seeking to increase the popularity of their musical compositions.
References
Amrhein, V., Trafimow, D., & Greenland, S. (2019). Inferential statistics as descriptive statistics: There is no replication crisis if we don’t expect replication. The American Statistician, 73(sup1), 262-270.
Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of Cardiac Anaesthesia, 22(1), 67-72.
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis. John Wiley & Sons.
Yu, Z., Guindani, M., Grieco, S. F., Chen, L., Holmes, T. C., & Xu, X. (2022). Beyond t test and ANOVA: Applications of mixed-effects models for more rigorous statistical analysis in neuroscience research. Neuron, 110(1), 21-35.
Appendix A — R Code Used
LMR <- lm(track_popularity ~ duration_min, data = spotify_data)
summary(LMR)
scatter_plot <- ggplot(spotify_data, aes(x = duration_min, y = track_popularity)) +
geom_point() +
geom_smooth(method = “lm”, se = FALSE) +
labs(title = “Scatter Plot and Regression Line”,
x = “Track Duration (minutes)”,
y = “Track Popularity”)
print(scatter_plot)
min(spotify_data$tempo)
max(spotify_data$tempo)
tempo_breaks <- c(0, 40, 80, 120, 160, 200, 240)
tempo_labels <- c(“low tempo”, “moderate tempo”, “medium tempo”, “high tempo”, “very high tempo”, “extreme tempo”)
spotify_data$tempo_cats <- cut(spotify_data$tempo, breaks = tempo_breaks, labels = tempo_labels, include.lowest = TRUE)
head(spotify_data)
cats_counts <- table(spotify_data$tempo_cats)
print(cats_counts)
tempo_breaks_new <- c(0, 60, 120, 180, 240)
tempo_labels_new <- c(“low tempo”, “medium-low tempo”, “medium-high tempo”, “high tempo”)
spotify_data$tempo_cats_new <- cut(spotify_data$tempo, breaks = tempo_breaks_new, labels = tempo_labels_new, include.lowest = TRUE)
cats_counts_new <- table(spotify_data$tempo_cats_new)
print(cats_counts_new)
anova_ress <- aov(track_popularity ~ tempo_cats_new, data = spotify_data)
summary(anova_ress)
boxplot_plot <- ggplot(spotify_data, aes(x = tempo_cats_new, y = track_popularity)) +
geom_boxplot() +
labs(title = “Boxplot for differences in track_popularity between tempo_category”,
x = “Tempo Category”,
y = “Track Popularity”)
print(boxplot_plot)
tukey_new <- TukeyHSD(anova_ress)
print(tukey_new)
result <- tapply(spotify_data$tempo, spotify_data$tempo_cats_new, function(x) c(mean = mean(x), sd = sd(x)))
print(result)
Appendix B — Results of Regression Analysis
Appendix C — Results of ANOVA Test
