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I have been looking around for and answer a while now and figured out how to make the entry in the multirowvisible. But now the entry is being shifted for some reason. Can you please help me? Down here I have a minimal working example.

documentclass[12pt]article
usepackage[utf8]inputenc
usepackage[swedish]babel
usepackagemultirow

usepackagecolor, colortbl

definecolorLightCyanrgb0.88,1,1

begindocument
begintable[h!]
centering

begintabularl
hline
Känsla & Elevgrupp & ''Gillade det ofta'' ($%$) & ''Övriga svar'' ($%$) & 
$U$-värde ($p<0.05$) \
hline
rowcolorLightCyan
Gillade Det & $1$ & $75$ & $25$ & \
rowcolorLightCyan
& $2$ & $37$ & $62$ & multirow2*$12.5$ \
hline
Fann det Vackert & $1$ & $cdots$ & $cdots$ & multirow2*$cdots$ \
& $2$ & $cdots$ & $cdots$ &\
hline
Var Imponerad & $1$ & $cdots$ & $cdots$ & multirow2*$cdots$ \
& $2$ & $cdots$ & $cdots$ &\
hline
Fascinerade Mig & $1$ & $cdots$ & $cdots$ & multirow2*$cdots$ \
& $2$ & $cdots$ & $cdots$ &\
hline


endtabular
captionExempel på beskrivande statistik med ett signifikanstest på elevers 
svar om hur ofta de kände att gillade problemet.
labeltabkors3
endtable
enddocument

And this is what it looks like:

If you replace 2 with -2 as in multirow-2*$12.5$ you will get the desired result.

With multirow2 you merge the cell in the current row with the cell in the following row. This is why your text overlaps with the horizontal line. Shifting the command ine row upwards is no solution since you are using rowcolor. So, instead you can use multirow-2 to merge the cell in the current wor with the cell in the previous row.

I'd also suggest to replace usepackagecolor,colortbl with usepackage[table]xcolor. Also, there is no need to use math mode for all the numbers. I have also removed that in the following MWE:

documentclass[12pt]article
usepackage[utf8]inputenc
usepackage[swedish]babel
usepackagemultirow

usepackage[table]xcolor

definecolorLightCyanrgb0.88,1,1

begindocument
begintable[h!]
centering

begintabularl
hline
Känsla & Elevgrupp & ''Gillade det ofta'' ($%$) & ''Övriga svar'' ($%$) & 
$U$-värde ($p<0.05$) \
hline
rowcolorLightCyan
Gillade Det & 1 & 75 & 25 &multirow2*12.5 \
rowcolorLightCyan
& 2 & 37 & 62 & \
hline
Fann det Vackert & 1 & $cdots$ & $cdots$ & multirow2*$cdots$ \
& 2 & $cdots$ & $cdots$ &\
hline
Var Imponerad & 1 & $cdots$ & $cdots$ & multirow2*$cdots$ \
& 2 & $cdots$ & $cdots$ &\
hline
Fascinerade Mig & 1 & $cdots$ & $cdots$ & multirow2*$cdots$ \
& 2 & $cdots$ & $cdots$ &\
hline
endtabular
captionExempel på beskrivande statistik med ett signifikanstest på elevers 
svar om hur ofta de kände att gillade problemet.
labeltabkors3
endtable
enddocument

Here is a second version of the MWE that uses tabularx and makecell to make the table fit into the textwidth:

documentclass[12pt]article
usepackage[utf8]inputenc
usepackage[swedish]babel
usepackagemultirow

usepackage[table]xcolor
usepackagemakecell
usepackagetabularx

definecolorLightCyanrgb0.88,1,1

begindocument
begintable[h!]
centering

begintabularxtextwidthl
hline
Känsla & Elevgrupp & makecell''Gillade det ofta''\ ($%$) & makecell''Övriga svar''\ ($%$) & 
makecell$U$-värde\ ($p<0.05$) \
hline
rowcolorLightCyan
 & $1$ & $75$ & $25$ & \
rowcolorLightCyan
multirow-2=Gillade Det & $2$ & $37$ & $62$ & multirow-2*$12.5$ \
hline
multirow2=Fann det Vackert & $1$ & $cdots$ & $cdots$ & multirow2*$cdots$ \
& $2$ & $cdots$ & $cdots$ &\
hline
multirow2=Var Imponerad & $1$ & $cdots$ & $cdots$ & multirow2*$cdots$ \
& $2$ & $cdots$ & $cdots$ &\
hline
multirow2=Fascinerade Mig & $1$ & $cdots$ & $cdots$ & multirow2*$cdots$ \
& $2$ & $cdots$ & $cdots$ &\
hline
endtabularx
captionExempel på beskrivande statistik med ett signifikanstest på elevers 
svar om hur ofta de kände att gillade problemet.
labeltabkors3
endtable

enddocument

I would redesign your table as follows:

Used are:

• removed vertical rules


• for horizontal rules are used rules from booktabs table; its numbers are significantly reduced


• columns with numbers are of S type (defined in siunitx package)

Edit:

• for aligning numbers in the last row is considered tablenum macro defined in the siunitx package

documentclass[12pt]article
usepackage[swedish]babel

usepackage[table]xcolor
usepackagebooktabs, makecell, multirow, tabularx
renewcommandtheadfontnormalsize
definecolorLightCyanrgb0.88,1,1
usepackagesiunitx

begindocument
 begintable[ht!]
centering
sisetuptable-format=2.2
begintabularxtextwidth X cSSc % <---
 toprule
theadKänsla
 & theadElevgrupp
 & thead''Gillade det ofta''\ ($%$) 
 & thead''Övriga svar''\ ($%$)
 & thead$U$-värde\ ($p<0.05$) \
 specialrulelightrulewidthaboverulesep0pt
rowcolorLightCyan
 & 1 & 75 & 25 & \
rowcolorLightCyan
multirow-2=Gillade Det
 & 2 & 37 & 62 & multirow-2*mrtf3.212.5 \ % <---
 specialrulelightrulewidth0ptbelowrulesep
multirow2=Fann det Vackert
 & 1 & $cdots$ & $cdots$ & multirow2*mrtf3.2123.45 \ % <---
 & 2 & $cdots$ & $cdots$ & \
 addlinespace
multirow2=Var Imponerad
 & 1 & $cdots$ & $cdots$ & multirow2*$cdots$ \ % insert mrft macro 
 % when cdot is replaced by number
 & 2 & $cdots$ & $cdots$ & \ addlinespace
multirow2=Fascinerade Mig
 & 1 & $cdots$ & $cdots$ & multirow2*$cdots$ \
 & 2 & $cdots$ & $cdots$ & \
 bottomrule
endtabularx
captionExempel på beskrivande statistik med ett signifikanstest på elevers
svar om hur ofta de kände att gillade problemet.
labeltabkors3
 endtable
enddocument