While hallucinations, delusions, and incoherent speech are all noted symptoms of schizophrenia- new feelings or behaviors not present in healthy people-, flat affect (a lack of emotional expression and decrease in talkativeness) is a noted negative symptom, something that healthy people have/do that schizophrenia sufferers do not.

The causes of schizophrenia are varied but one of the leading suspected factors is an excess of the chemical dopamine.

A negative symptom is a symptom that represents something that the sufferer does not have but is regularly found in unaffected people. In the case of a schizophrenic, he or she may not display any emotion where an unaffected person would. This is known as a "flat effect.” 

There are four types of schizophrenia, one of them being paranoid schizophrenia. The identifying and differentiating symptom of paranoid schizophrenia is the delusion that someone or something is “out to get” the person with the disorder.

A schizophrenic is susceptible to certain kinds of delusions—namely those of grandeur, reference, and persecution. Delusions of grandeur lead the schizophrenic to believe they are greater than they are such as thinking they are a prophet or a god. Those of reference may lead them to believe secret messages are being sent to them and they must decode them. Those of persecution incite the paranoid belief that people are out to get them.

A positive symptom is something that is present in the affected person that is not normally found in unaffected persons. Essentially, it's not positive in the sense of "good" but of something being added. One out of several positive symptoms of schizophrenia is the presence of delusional thinking, where one thinks there are things that are present that actually are not.

A positive symptom is a gained behavior, while a negative symptom is a loss of normal function. The gained paranoia behaviors are therefore 'positive.'

Schizophrenia is marked by several unique brain traits, including: 

Enlarged ventricles 

Small/disorganized hippocampus

Small amygdala

The absence of a cerebellum would result in serious motor function deficits, but is absolutely not characteristic of the brains of patients with schizophrenia.

Many people with schizophrenia have hallucinations, which can be defined as sensory experiences without sensory stimulation. Although auditory, visual, tactile (touch), gustatory (taste), and olfactory (smell) hallucinations are all possible, auditory hallucinations, particularly hearing voices that no one else can hear, are by far the most common.

Schizophrenia has positive symptoms (characteristics that do not exist in neurotypical people) and negative symptoms (the lack of something that neurotypical people have). Therefore, hallucinations or delusions are a positive symptom, whereas flat affect (lack of facial expressions), apathy (lack of passion), avolition (lack of motivation), and monotone speech (lack of tone variance in speech) are all negative symptoms.