How to fix unsupported_db_table_row_format in moodle - Converting InnoDB tables to Barracuda

Here is a Unix "screen-shot":

$ cd /path/to/your/moodle
$ php admin/cli/mysql_compressed_rows.php
Script for detection of row size problems in MySQL InnoDB tables.

By default InnoDB storage table is using legacy Antelope file format
which has major restriction on database row size.
Use this script to detect and fix database tables with potential data
overflow problems.

Options:
-i, --info Show database information
-l, --list List problematic tables
-f, --fix Attempt to fix all tables (requires SUPER privilege)
-s, --showsql Print SQL statements for fixing of tables
-h, --help Print out this help

Example:
$ sudo -u www-data /usr/bin/php admin/cli/mysql_compressed_rows.php -l

$ php admin/cli/mysql_compressed_rows.php -l
mdl_data Compact (needs fixing)
mdl_data_fields Compact (needs fixing)
mdl_enrol_paypal Compact (needs fixing)
mdl_lti Compact (needs fixing)
mdl_user Compact (needs fixing)
mdl_user_info_field Compact (needs fixing)

$ php admin/cli/mysql_compressed_rows.php -f
Cannot enable GLOBAL innodb_file_per_table setting, use --showsql option and execute the statements manually.!!! Error writing to database !!!

$ php admin/cli/mysql_compressed_rows.php -s
Copy the following SQL statements and execute them using account with SUPER privilege:

USE moodle27;
SET SESSION sql_mode=STRICT_ALL_TABLES;
SET GLOBAL innodb_file_per_table=1;
SET GLOBAL innodb_file_format=Barracuda;
ALTER TABLE mdl_data ROW_FORMAT=Compressed;
ALTER TABLE mdl_data_fields ROW_FORMAT=Compressed;
ALTER TABLE mdl_enrol_paypal ROW_FORMAT=Compressed;
ALTER TABLE mdl_lti ROW_FORMAT=Compressed;
ALTER TABLE mdl_user ROW_FORMAT=Compressed;
ALTER TABLE mdl_user_info_field ROW_FORMAT=Compressed;

$ mysql -u root -p
Enter password: [invisible]
Welcome to the MySQL monitor.
[...]
mysql> use dbname;
Database changed
mysql> SET SESSION sql_mode=STRICT_ALL_TABLES;
Query OK, 0 rows affected (0.00 sec)

mysql> SET GLOBAL innodb_file_format=Barracuda;
Query OK, 0 rows affected (0.00 sec)

mysql> ALTER TABLE mdl_data ROW_FORMAT=Compressed;
Query OK, 0 rows affected, 2 warnings (0.04 sec)
Records: 0 Duplicates: 0 Warnings: 2

[...] 

Yes, the "sudo -u www-data" part in the example line:
$ sudo -u www-data /usr/bin/php admin/cli/mysql_compressed_rows.php -l 
is unnecessary! (The php script ultimately sends SQL commands to the database which is controlled by the user management of the database, not the Unix shell.) 

Note on type setting:
normal: what programs print on the screen
bold: what you type
bold slanted: you type them adjusting to your setup.