The imaging of neuronal activity using calcium indicators has become a staple of modern neuroscience. However, without ground truths, there is a real risk of missing a significant portion of the real responses. Here, we show that a common assumption, the non-negativity of the neuronal responses as detected by calcium indicators, biases all levels of the frequently used analytical methods for these data. From the extraction of meaningful fluorescence changes to spike inference and the analysis of inferred spikes, each step risks missing real responses because of the assumption of non-negativity. We first show that negative deviations from baseline can exist in calcium imaging of neuronal activity. Then, we use simulated data to test three popular algorithms for image analysis, CaImAn, suite2p, and CellSort, finding that suite2p may be the best suited to large datasets. We also tested the spike inference algorithms included in CaImAn, suite2p, and Cellsort, as well as the dedicated inference algorithms MLspike and CASCADE, and found each to have limitations in dealing with inhibited neurons. Among these spike inference algorithms, FOOPSI, from CaImAn, performed the best on inhibited neurons, but even this algorithm inferred spurious spikes upon the return of the fluorescence signal to baseline. As such, new approaches will be needed before spikes can be sensitively and accurately inferred from calcium data in inhibited neurons. We further suggest avoiding data analysis approaches that, by assuming non-negativity, ignore inhibited responses. Instead, we suggest a first exploratory step, using k-means or PCA for example, to detect whether meaningful negative deviations are present. Taking these steps will ensure that inhibition, as well as excitation, is detected in calcium imaging datasets.