Your problem is that you have different names for each switch so that they are grouped together, they should have the same name, it looks like you are confusing the name and value.
<body>
<form name="search_form" id="search_form" method="POST" action="search_user_data.php">
<table border="1">
<tr>
<td colspan="2">
<input type="text" id="search" name="search" />
</td>
<td>
<input type="submit" value="Search"/>
</td>
</tr>
<tr>
<td>
<input type="radio" name="searchType" value="id_radio"/>ID
</td>
<td>
<input type="radio" name="searchType" value="surname_radio"/>Surname
</td>
<td>
<input type="radio" name="searchType" value="dob_radio"/>DoB
</td>
</tr>
</table>
</form>
</body>
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