Teen gambling

Introduction

This analysis examines factors influencing teenage gambling expenditure. We explore the relationships between annual expenditure, gender, and weekly income. Our hypothesis is that both gender and income affect teenagers’ gambling expenditure.

Data

The analysis uses data from (Ide-Smith and Lea 1988), a survey of teenage gambling behaviour in Britain.

The key variables are:

sex
status : Socioeconomic status score based on parents’ occupation
income : Weekly income in pounds
verbal : Verbal score (number of words defined correctly, out of 12)
gamble : Annual expenditure on gambling in pounds

sex	status	income	verbal	gamble
female	51	2.00	8	0.0
female	28	2.50	8	0.0
female	37	2.00	6	0.0
female	28	7.00	4	7.3
female	65	2.00	8	19.6
female	61	3.47	6	0.1

A cursory look at the data suggests that females likely spend less on gambling compared to males. Additionally, most females do not spend more than approximately £20 per year on gambling.

There also seems positive association between income and amount spent on gambling (at least for males). This is not very surprising as one would expect that individuals with higher income would be able to spend more on gambling.
From what this plot indicates, it may be worth evaluating if there is a differential effect of income based on gender.

Analysis

The response variable gamble is non‑negative and strongly right‑skewed. We therefore model log(gamble + 1). Adding £1 ensures the log is defined for zero spenders, keeps small expenditures near zero on the transformed scale, and avoids introducing artificial extreme negative values. Note this is different from a GLM with a log link: here we model the (logged) response directly, which changes how effects are interpreted on the original scale.

Observation 24 (gamble = £156) appears to be an outlier and is removed from the analysis.

Effect of Gender

It seems plausible that males are spending more on gambling compared to females. This is also indicated by the boxplot below. We will evaluate this hypothesis using a simple linear model with log(gamble + 1) as response and sex as explanatory variable.

Analysis of Variance Table

Response: log_gamble
          Df Sum Sq Mean Sq F value   Pr(>F)   
sex        1 20.365  20.365  12.261 0.001074 **
Residuals 44 73.085   1.661                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Gender seems to have statistically significant association with gambling expenditure.
Anova procedure is equivalent to a t-test with constant variance assumption (Faraway 2025), which seems fair from the Boxplot above. They test for the same effect and result in identical p-values.

Before moving to analysing joint effect of Income and Gender, it is imperative to check if the effect of gender is not due to confounding by income. It could well be the case that individuals with higher income spend more on gambling. But then if high income itself is associated with gender, then the above effect of gender may be spurious. We will explore this next.

Analysis of Variance Table

Response: income
          Df Sum Sq Mean Sq F value Pr(>F)
sex        1   4.58  4.5754  0.3685 0.5469
Residuals 44 546.25 12.4149

The above plot and the test indicates that income is not significantly associated with gender and hence does not mask its effect on gambling expenditure.

For the analysis that follows, we shall print the summary of gender only model to show the Estimate value and Std. Error of gender.

summary(gender_model)


Call:
lm(formula = log_gamble ~ sex, data = teengamb)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.4630 -1.0616  0.1547  1.0979  2.0478 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   1.1117     0.2957   3.760 0.000498 ***
sexmale       1.3513     0.3859   3.502 0.001074 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.289 on 44 degrees of freedom
Multiple R-squared:  0.2179,    Adjusted R-squared:  0.2002 
F-statistic: 12.26 on 1 and 44 DF,  p-value: 0.001074

Effect of Gender and Income

With income variable included alongside sex, the effect of sex remains significant (although is reduced from 1.35 to 1.24 with lower Std. Error).
Income itself is significantly associated with gambling expenditure.
The intercept is non-significant indicating that for reference class (female), gambling expenditure is likely 0£ if they have close to 0 income and it makes intuitive sense (although for adults and addicts this may not necessarily be true).
This model does not include an interaction between sex and income for simplicity, yet it fits the data well. Model diagnostics appear acceptable.


Call:
lm(formula = log_gamble ~ sex + income, data = teengamb)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.2327 -0.7944  0.1318  0.8419  2.2973 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.37092    0.33009   1.124 0.267373    
sexmale      1.23699    0.34216   3.615 0.000782 ***
income       0.17852    0.04869   3.667 0.000671 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.138 on 43 degrees of freedom
Multiple R-squared:  0.4042,    Adjusted R-squared:  0.3765 
F-statistic: 14.59 on 2 and 43 DF,  p-value: 1.46e-05

Additionally, the residuals do not indicate any obvious pattern with respect to gender.

From earlier plots we suspected a possible differential effect of income by gender. Fitting an interaction did not improve fit and the interaction term is not significant, so the simpler additive model is preferred.

Analysis of Variance Table

Model 1: log_gamble ~ sex * income
Model 2: log_gamble ~ sex + income
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     42 53.517                           
2     43 55.676 -1   -2.1582 1.6938 0.2002

Additionally, interaction term is not significant and so it is best to remove it and keep the model simple.


Call:
lm(formula = log_gamble ~ sex * income, data = teengamb)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.1894 -0.9791  0.0763  0.8456  2.0447 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)  
(Intercept)     0.85855    0.49761   1.725   0.0918 .
sexmale         0.58832    0.60303   0.976   0.3348  
income          0.06101    0.10240   0.596   0.5545  
sexmale:income  0.15114    0.11613   1.301   0.2002  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.129 on 42 degrees of freedom
Multiple R-squared:  0.4273,    Adjusted R-squared:  0.3864 
F-statistic: 10.45 on 3 and 42 DF,  p-value: 2.921e-05

Conclusion

Both gender and income are significantly associated with teenage gambling expenditure. Males spend about three times more than females on average (note: reporting biases could inflate this effect; boys may over-report and girls may under-report (Ide-Smith and Lea 1988)). A £1 increase in weekly income is associated with an approximate 19% increase in annual gambling expenditure on the log scale interpretation. The interaction between gender and income was not significant, suggesting the effect of income is similar across genders.

References

Faraway, Julian J. 2025. Linear Model with r, Third Edition. CRC Press.

Ide-Smith, Susan G., and Stephen E. G. Lea. 1988. “Gambling in Young Adolescents.”