You can use the t-statistic formula to test the hypothesis. Student's t test when independent groups are subjected to the comparison under the assumptions of normal distribution and equal variances (or standard deviation). In a condition of unequal variances we may apply the Welch's t test as an adaptation of the t test. The t statistic is the ratio of mean difference and standard errors of the mean difference. For a comparison of more than two group means, the one-way analysis of variance (ANOVA) also can be used.

Following links shows an example of caculation and formulas too.

Good Luck.

Article Analysis of variance (ANOVA) comparing means of more than two groups

https://www.researchgate.net/post/Three_means_comparison_by_t_test_or_ANOVA

You can use Stata (Statistical Software) and conduct mean comparison t test. If the data is in pairs then you can use the mean comparison t test for paired data. You have to make sure your data meets the preconditions and assumptions of the tests you want to apply. Youtube lessons are available and you can also consult stata list i.e. stata community online for any help.

Regards,

Szymon Stereńczak sir are you suggesting me to run my model with fixed or random effects with dummies taken as independent variable and profitability as depedent variable?

All interventions are to be considered with great interest. A comparison test of the means between more than two groups is based on the Fisher statistic (if the profitability variances are the same between the groups of banks, which I strongly doubt) or on the Welch statistic (non-group variances not homogeneous). The student statistic is used to make the inference of a comparison of mean over two groups under the homogeneity hypothesis of the variances.

As Professor Szymon Stereńczak pointed out, an average comparison test is not enough to test a hypothesis on panel data; the individual heterogeneity must be checked and may be even temporal according to the specification test results to be made: Hisiao, Breuch-Pagan, then a test CD or a Hausman test. I think that, given the strong individual heterogeneity of banks, you will be led to specify a model with fixed individual effects. The variables to be controlled for the study of performance in general are: the size of the entity, its level of indebtedness / financial autonomy, its level of risk (standard deviation of returns), its degree of diversification ( bank, bank-insurance, bank-insurance, portfolio management, etc.), its stock market listing, number of financial markets where it is listed, its governance system (size of the board of directors, fraction of independent directors), membership of bank to a group, existence of structures with minority control (control pyramids, share classes, etc.), nationality of the registered office, number of subsidiaries of the bank); we do not worry you do not have to control all these variables since you control fixed effects. If by chance random exogenous variables are stable over time, you will have the problem of perfect collinearity, in this case either you use the generalized moment estimators of Blundell and Bond in equation system, or the new estimator of Powell under stata xtqregpd

Thank you for all those who intervened.

All interventions are to be considered with great interest. A comparison test of the means between more than two groups is based on the Fisher statistic (if the profitability variances are the same between the groups of banks, which I strongly doubt) or on the Welch statistic (non-group variances not homogeneous). The student statistic is used to make the inference of a comparison of mean over two groups under the homogeneity hypothesis of the variances.

As Professor Szymon Stereńczak pointed out, an average comparison test is not enough to test a hypothesis on panel data; the individual heterogeneity must be checked and may be even temporal according to the specification test results to be made: Hisiao, Breuch-Pagan, then a test CD or a Hausman test. I think that, given the strong individual heterogeneity of banks, you will be led to specify a model with fixed individual effects. The variables to be controlled for the study of performance in general are: the size of the entity, its level of indebtedness / financial autonomy, its level of risk (standard deviation of returns), its degree of diversification ( bank, bank-insurance, bank-insurance, portfolio management, etc.), its stock market listing, number of financial markets where it is listed, its governance system (size of the board of directors, fraction of independent directors), membership of bank to a group, existence of structures with minority control (control pyramids, share classes, etc.), nationality of the registered office, number of subsidiaries of the bank); we do not worry you do not have to control all these variables since you control fixed effects. If by chance random exogenous variables are stable over time, you will have the problem of perfect collinearity, in this case either you use the generalized moment estimators of Blundell and Bond in equation system, or the new estimator of Powell under stata xtqregpd

Thank you for all those who intervened

Dilesha Rathnayake mam can i apply anova on panel data

Naina Grover , Yes you can apply.