Try
<form name="yourform" action="<?php echo $_SERVER['PHP_SELF']; ?>" method="post">
<input checked="unchecked" type="Radio" name="gender" value="male" class="auto-style3" style="width: 20px">Male
<input checked="unchecked" type="Radio" name="gender" value="female">Female
<input type="submit" value="Submit">
</form>
<?php
if ( $_SERVER['REQUEST_METHOD'] == 'POST' ) {
$answer = $_POST['gender'];
if ($answer == "male") { ?>
<select name="Select1">
<option></option>
<option>Floor</option>
<option>Pommel</option>
<option>Rings</option>
<option>Vault</option>
<option>P Bars</option>
<option>High Bar</option>
</select>
<?php } else { ?>
<select name="Select1">
<option></option>
<option>Vault</option>
<option>Uneven Bars</option>
<option>Beam</option>
<option>Floor</option>
</select>
<?php }} ?>
This will only work if you have posted the result of the "gender" radio, of course, since php is executed on server-side...