Wi-Fi turned off but battery usage shows shows huge drain from it I have a problem with my Galaxy S3 4G. It's currently all stock and running Android 4.4.4.

It seems the Wi-Fi will not turn off i.e. I can turn it "off" in the settings or notification bar, and this will stop Wi-Fi from being connected and device uses my mobile data instead, however in the battery menu the Wi-Fi is still being shown as on, even when it's turned off. 

As you can see in the attached image, it's draining my battery really fast, and will only turn off when the device is in flight mode. I've checked and cannot see any rogue apps causing this, but after searching online and checking all option menus I seem unable to fix this problem. 

Is there any way to stop this, save for a factory reset? Is this a KitKat wide problem, or just on my phone?

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This is a common misconception with Android. When you turn off Wi-Fi, Wi-Fi does not actually turn off. There is an advanced settings menu where you will find an option that either says Wi-Fi scanning or Wi-Fi always on. Google uses Wi-Fi points to determine the device's location without activating the GPS.

Turn Wi-Fi scanning off to fix this. You might want to turn off Wi-Fi while asleep while your at it. It's in the same menu.

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Edit: In Android 6.0 (Marshmallow), this option has been moved. It is now located in Location > (Overflow menu) > Scanning (Thanks, nanny)