# Calculation and relevance of t-statistic in the event study methodology

Statistical measures, particularly the T-statistic, serve as crucial tools in diverse research domains, including economics, finance, and genetics. The T-statistic plays a pivotal role in quantifying the significance of relationships between variables by comparing sample means to data variability. Its application enables researchers to discern whether observed associations are statistically meaningful or a result of chance.

A high T-statistic signifies a robust link, while a low one indicates a weak connection. This statistical tool enhances research rigor by facilitating informed decisions about the presence or absence of meaningful relationships between variables, contributing to more accurate and credible research. In the context of examining the impact of result announcements on stock prices, T-statistics are indispensable. They aid in differentiating between genuine price effects caused by announcements and random data fluctuations. This article delves into the calculation of T-statistics for assessing the impact of result announcements on stock prices.

## Significance of T-statistic in stock price announcements

T-statistics are employed to assess the statistical significance of the impact of announcements on stock prices. This helps determine whether observed price changes are likely due to the announcement rather than random market fluctuations, providing robust evidence of announcement effects (Elangovan et al., 2022; Pandey et al., 2022). Movements that follow important announcements, like those on earnings or mergers.

To verify that the observed price changes are statistically significant and not just random fluctuations, researchers compute t-statistics. A high t-statistic in this situation suggests that relevant information, rather than a random chance caused the market to react to the announcement. This aids in decision-making and provides information to investors and analysts to assess the impact of news on stock prices (Elangovan et al., 2022; Pandey et al., 2022).

## Computing T-statistics and standard error

The working for computation of t-statistics and assessing result announcement impact began by collecting the data as per result announcement date for FY 2018-23. Once the data was collected, all required variables such as; return, market return value, expected return, abnormal return and average abnormal return were computed. Based on the computed information, T-statistic based testing was done for the returns using Stata as the tool of analysis. Herein, the formula ’s used for computation of value were as follows:

T-statistic of abnormal return/average abnormal return

AR / AAR = Abnormal return /Average abnormal return

σ (AR /AAR ) = Standard error of abnormal return /Average abnormal return

## The statistical value of average abnormal return in the Energy Sector

Time period | T-2 | T-1 | T | T+1 | T+2 |
---|---|---|---|---|---|

T statistics | 110.33 | -0.39 | -1.43 | -3.43 | -2.81 |

standard error | -13.16 | -13.16 | -13.16 | -13.16 | -13.16 |

The above table shows that the standard error value for the energy sector average abnormal return was **13.156** based on which the value of t-statistic was computed. The value of standard error was more than 1, which represents some error presence but still as the value was low thus, the results computed would be adequate. Herein, approximately the absolute t-statistic value of T-2, T+1 and T+2 is **more than 1.96** (the t-critical value at 95% of confidence interval), while for T-1 and T the approximate value is low.

T statistics value of abnormal return for Energy Sector.

Company name | T-2 | T-1 | T | T+1 | T+2 |
---|---|---|---|---|---|

adani green energy | -0.16 | 0.19 | -1.71 | -1.01 | 0.11 |

adani power | 0.04 | 0.03 | 0.04 | 0.07 | -0.07 |

adani transmission | 0.49 | 0.04 | 0.61 | 1.01 | -0.89 |

Bhel | 96.77 | 0.00 | -0.07 | -0.01 | -0.04 |

guj ind power | 0.06 | 0.00 | -0.02 | -0.07 | -0.04 |

gvk power | 0.03 | 0.03 | 0.01 | 0.04 | 0.01 |

indian energy exchange | -0.15 | -0.12 | -0.15 | -0.44 | -0.19 |

jaiprakash pow | 0.03 | -0.04 | 0.05 | -0.03 | -0.02 |

jsw energy | -0.03 | -0.57 | 0.02 | -0.07 | 0.02 |

kec international | 0.07 | 0.20 | -0.14 | 0.04 | -0.21 |

kirloskar ind | -0.76 | -0.03 | 0.46 | -2.99 | 0.45 |

NHPC | 0.01 | -0.01 | 0.04 | -0.01 | -0.03 |

NTPC | -0.02 | 0.05 | 0.05 | -0.03 | -0.02 |

power grid | 0.09 | 0.00 | -0.09 | -0.11 | 0.01 |

rattan power | 0.03 | 0.01 | 0.03 | 0.09 | -0.01 |

reliance infra | -0.15 | 0.01 | -0.10 | -0.07 | -0.23 |

reliance power | -0.01 | 0.07 | 0.06 | 0.09 | 0.05 |

SE power | 0.04 | 0.06 | 0.04 | 0.00 | 0.00 |

tata power | 0.01 | -0.04 | 0.00 | -0.02 | -0.06 |

thermax | 0.28 | -0.16 | -0.22 | -0.66 | -0.98 |

The above table shows that for each of the company the t-statistic value is different. Only for some companies and only for some specific times like; the absolute T-statistic value is **more than 1.96** for Bhel at T-2 or Kirloskar Ltd at T+1. So, the variation due to result announcement can be observed for some companies in the energy sector.

## The t-statistic value for average abnormal return in the pharma sector

Time period | T-2 | T-1 | T | T+1 | T+2 |
---|---|---|---|---|---|

T statistics | 106.75 | 1.95 | -1.51 | -1.92 | -2.03 |

standard error | -27.89 | -27.89 | -27.89 | -27.89 | -27.89 |

For the pharma sector too, there is existence of error in computation which is even more than the energy sector, as the number of companies included are more. However, as the value is **less than 100**, so herein, the impact assessment would be appropriate. The absolute value of T-statistic for T-2, T+1, T+2 again are **more than 1.96** but for T-1 and T is **less than 1.96**.

As the list of companies in pharma sector was more, so the division of companies was done in 2 groups. Herein for 2^{nd} group the T-statistic values are:

Time period | T-2 | T-1 | T | T+1 | T+2 |
---|---|---|---|---|---|

T statistics | -23.55 | -121.72 | -0.17 | -4.27 | 5.40 |

Standard error | -22.57 | -22.57 | -22.57 | -22.57 | -22.57 |

^{nd}group)

In the 2^{nd} group, the value of standard error is low showing less error chances and the values of T-statistics show improvement. For T-2, T-1, T+1, and T+2 the absolute value of T-statistic are **more than 1.96** showing possibility of impact assessment.

Further, the abnormal return value’s T-statistic examination is presented below.

Company name | T-2 | T-1 | T | T+1 | T+2 |
---|---|---|---|---|---|

aarti drugs | -0.14 | 0.28 | 0.08 | -0.44 | -0.05 |

abbott india | -3.87 | -1.62 | 2.06 | -3.43 | 3.92 |

alpa labs | 0.02 | 0.04 | 0.02 | -0.01 | 0.01 |

ami organics | -0.13 | 0.20 | -0.56 | 0.13 | -0.81 |

astrazeneca | 0.47 | -0.05 | 0.08 | -1.18 | 0.01 |

bajaj healthcare | 0.15 | -0.10 | -0.16 | -0.01 | -0.18 |

biocon | -0.08 | 0.02 | -0.04 | -0.11 | 0.01 |

biofil chemicals | 0.04 | 0.04 | 0.06 | 0.01 | 0.03 |

dr reddys | -0.50 | -0.59 | -0.51 | -0.29 | 0.22 |

gland pharma | -0.37 | -0.69 | 0.16 | 0.64 | 0.63 |

Gufic biosciences | 0.02 | -0.03 | 0.00 | -0.05 | -0.09 |

hikal | -0.01 | 0.11 | -0.04 | 0.09 | -0.11 |

indoco remedies | 0.06 | 0.01 | -0.12 | 0.06 | -0.10 |

ind-swift labs | 0.02 | 0.01 | 0.02 | 0.04 | -0.03 |

IOL chemicals | 0.09 | -0.01 | -0.18 | -0.30 | -0.20 |

ipca labs | -0.10 | 0.14 | -0.03 | 0.11 | -0.02 |

jagsonpal pharma | 0.05 | 0.02 | 0.08 | 0.02 | 0.05 |

jubliant pharmo | 0.14 | -0.06 | -0.04 | -0.07 | 0.04 |

kilitch drugs | 0.02 | -0.03 | 0.07 | -0.03 | 5.60 |

kopran | 0.03 | 0.04 | 0.00 | -0.01 | 0.02 |

laurus labs | 0.03 | 0.03 | -0.04 | 0.32 | 0.07 |

lincoln pharma | 0.10 | -0.03 | -0.12 | -0.09 | 0.01 |

lupin | 0.02 | 0.00 | -0.09 | -0.12 | -0.15 |

mangalam drugs | 0.01 | 0.04 | 0.06 | 0.01 | 0.02 |

medicamen | 0.07 | 0.02 | -0.52 | -0.16 | -0.21 |

Morepen Labs | 98.94 | -0.01 | -0.10 | 0.48 | -0.13 |

natco pharm | 0.01 | 0.06 | -0.25 | -0.35 | -0.17 |

nectar lifesciences | 0.00 | 0.04 | 0.02 | 0.03 | 0.00 |

NGL fine chem | -1.17 | -0.44 | 0.02 | 0.40 | -0.51 |

Orchid Pharma | -0.04 | 0.08 | -0.02 | -0.10 | 0.02 |

pfizer | 1.10 | 0.69 | -0.52 | 0.04 | -0.02 |

sanofi india | -1.23 | -75.35 | 0.08 | 1.79 | 0.30 |

sequent sc | 0.10 | 0.02 | -0.03 | -0.02 | 0.03 |

shilpa medicare | 0.02 | 0.06 | -0.19 | -0.12 | 0.19 |

solara active | 0.18 | 1.05 | -0.25 | -1.01 | -0.12 |

suven life sc | 0.08 | 0.07 | 0.02 | 0.05 | 0.04 |

syngene | -0.03 | -0.03 | -0.06 | -0.06 | -0.18 |

themis medicare | -0.20 | 0.29 | -0.02 | -0.20 | 0.13 |

unichem labs | 0.00 | 0.09 | -0.11 | 0.03 | -0.01 |

windlas biotech | 0.02 | 0.04 | 0.04 | 0.00 | 0.13 |

wockhardt | -0.04 | 0.14 | -0.16 | -0.10 | 0.00 |

zim labs | -0.58 | 0.03 | 0.07 | -0.04 | -0.01 |

Even in the pharma sector very few companies have a value **more than 1.96**. Some of these are Abbott India in T-2, T, T+1, and T+2; Kilitich drugs in T+2; Morphen Labs in T-2; and Sanofi India in T-1. Thus, the number of time periods wherein impact could be seen in the pharma sector is more than energy sector.

## Conclusion

The computation of the t-statistic was necessary to determine the statistical significance of the results. It helped to assess whether the observed differences are likely due to the treatment or if they could have occurred by chance, providing confidence in the research findings. The t-statistic value in the energy sector is lower than pharma sector revealed that the result announcement impact was more for the pharma sector. The number of companies with significant T-statistic are more for pharma showing that pharma companies individually are more affected by result announcement.

#### References

- Elangovan, R., Irudayasamy, F. G., & Parayitam, S. (2022). Month‑of‑the‑Year Effect: Empirical Evidence from Indian Stock Market. Asia-Pacific Financial Markets, 29(3), 449–476. https://doi.org/10.1007/s10690-021-09356-2
- Pandey, D. K., Kumari, V., & Tiwari, B. K. (2022). Impacts of corporate announcements on stock returns during the global pandemic : evidence from the Indian stock market. Asian Journal of Accounting Research, April. https://doi.org/10.1108/AJAR-06-2021-0097

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