This study considers method of constructing tests for the hypotheses on scale parameters of generalized inverted family of distributions under progressive censoring. We derive three test statistics Q,U and The performance of these statistics, in terms of power, is studied through simulation for different values of scale parameter of generalized inverted exponential distribution, generalized inverted Rayleigh distribution and generalized inverted half-logistic distribution. For all these distributions, the test  performs better than the other tests when the scale parameter is greater than the value under null hypothesis and U performs better when the scale parameter is lesser than the value under null hypothesis.

generalized inverted exponential distribution, generalized inverted Rayleigh distribution, generalized inverted half-logistic distribution, progressive type-II censoring scheme, scale parameter, conditional distribution, quadratic form, power of the test.