AWK simple line replacement - awk

Question

How do I get AWK to correctly exchange the values of data file for the string "greater" (than before) or "smaller" (than before)"?
I'm trying:
awk '{if ($1>prev); print ($1="greater"); prev="smaller"}' arraydatafile
arraydatafile file:
2
7
6
1
7
3
Desired output:
smaller
greater ##### because 7 is greater than previous which is 2 ..
smaller ##### because 6 is smaller than previous which is 7 ..
smaller ##### because 1 is smaller than previous which is 1 ..
greater ##### etc etc
smaller
I get a jarbled thing instead.
Extremely grateful for your insight on this.
UPDATE:
Theres a new data file for clarification of the task at hand:
arraydatafile:
2
7
6
6
1
7
3
desired output
smaller
greater
smaller
equal ##### will remove it later, would be nice if this could be done right from the script or one liner preferrably though
smaller
greater
smaller
How do I get a one liner that does this in AWK? Its just comparing the previous ones to the next ones and telling what they are in comparison to them. Ill then delete the "equal" output lines with another one liner instead of complicating this little script, in order to simplify the current task at hand.
The script replace.awk:
#!/bin/awk -f
NR>1 {
if($1==p){
# Skip identical lines
next
}
if($1>p){
print "smaller"
}else{
print "greater"
}
}
# Store previous value
{p=$1}
ran on the arraydatafile
7
6
6
1
7
3
yields the following
root#debian:/home/user/Documents/# awk -f replace.awk arraydatafile
smaller
greater
greater
smaller
greater
How do I get the desired output instead?

Answer 1

Like this:
NR>1 {
if($1==p){
# Skip identical lines
next
}
if($1>p){
print "smaller"
}else{
print "greater"
}
}
# Store previous value
{p=$1}