I claim my student (529 & 1098-T require it). My student worked full time. Is he allowed the standard deduction (both Federal & Missouri), or is the amount reduced?

Your college student can file his own tax return even if he is your dependent.   He gets his standard deduction---which might be affected by the amount he earned.  He MUST say on his own return that he can be claimed as a dependent on someone else's tax return.

The standard deduction amount for an individual who may be claimed as a dependent by another taxpayer cannot exceed the greater of $1,100 or the sum of $400 and the individual’s earned income (not to exceed the regular standard deduction amount).

Your standard deduction lowers your taxable income.  It is not a refund.  You will see your standard or itemized deduction amount on line 12 of your 2022 Form 1040.

2022 STANDARD DEDUCTION AMOUNTS

SINGLE $12,950  (65 or older + $1750)

MARRIED FILING SEPARATELY $12,950  (65 or older + $1750)

MARRIED FILING JOINTLY $25,900  (65 or older + $1400 per spouse)

HEAD OF HOUSEHOLD  $19,400  (65 or older +$1750)

Legally Blind + $1750

@davefeltz - everyone gets a 'standard deduction' option. 

As long as your child checked the 'I can be claimed by someone else' button, the standard deduction is calculated differently that it is for you, but there is still a 'standard deduction' never-the-less. 

HOWEVER, if the student's income is high enough (exceeds $12950 for 2022)  that standard deduction is the same as it would be for anyone else filing Single. 

Q. Is he, as my dependent,  allowed the standard deduction, or is the amount reduced?

A. Simple answer: the amount is reduced. Dependents do not automatically get the full $12,950 standard deduction.  They get a reduced standard deduction, which is the greater of $1150 (2022) or their earned income plus $400.  So, if the student-dependent has enough earned income, it is possible for him to get the full $12,950 standard deduction. 

For others reading this, be aware that taxable scholarship is  a hybrid between earned and unearned income. It is earned income for purposes of the $12,950 filing requirement and the dependent standard deduction calculation (earned income + $400).  It is not earned income for the kiddie tax and other purposes (e.g. EIC).  For grad students and post grad fellows (but not undergrads), scholarship, stipend and fellowship income is also earned income ("compensation") for IRA contributions.