Analysis of variance ANOVA perform which type of test.
Answers
Answer:
A t-test compares means, while the ANOVA compares variances between populations. You could technically perform a series of t-tests on your data. ... ANOVA will give you a single number (the f-statistic) and one p-value to help you support or reject the null hypothesis.
ᴀɴᴀʟʏsɪs ᴏғ ᴠᴀʀɪᴀɴᴄᴇ (ᴀɴᴏᴠᴀ)
ᴀɴᴀʟʏsɪs ᴏғ ᴠᴀʀɪᴀɴᴄᴇ (ᴀɴᴏᴠᴀ) ɪs ᴀɴ ᴀɴᴀʟʏsɪs ᴛᴏᴏʟ ᴜsᴇᴅ ɪɴ sᴛᴀᴛɪsᴛɪᴄs ᴛʜᴀᴛ sᴘʟɪᴛs ᴀɴ ᴏʙsᴇʀᴠᴇᴅ ᴀɢɢʀᴇɢᴀᴛᴇ ᴠᴀʀɪᴀʙɪʟɪᴛʏ ғᴏᴜɴᴅ ɪɴsɪᴅᴇ ᴀ ᴅᴀᴛᴀ sᴇᴛ ɪɴᴛᴏ ᴛᴡᴏ ᴘᴀʀᴛs: sʏsᴛᴇᴍᴀᴛɪᴄ ғᴀᴄᴛᴏʀs ᴀɴᴅ ʀᴀɴᴅᴏᴍ ғᴀᴄᴛᴏʀs. ᴛʜᴇ sʏsᴛᴇᴍᴀᴛɪᴄ ғᴀᴄᴛᴏʀs ʜᴀᴠᴇ ᴀ sᴛᴀᴛɪsᴛɪᴄᴀʟ ɪɴғʟᴜᴇɴᴄᴇ ᴏɴ ᴛʜᴇ ɢɪᴠᴇɴ ᴅᴀᴛᴀ sᴇᴛ, ᴡʜɪʟᴇ ᴛʜᴇ ʀᴀɴᴅᴏᴍ ғᴀᴄᴛᴏʀs ᴅᴏ ɴᴏᴛ. ᴀɴᴀʟʏsᴛs ᴜsᴇ ᴛʜᴇ ᴀɴᴏᴠᴀ ᴛᴇsᴛ ᴛᴏ ᴅᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ɪɴғʟᴜᴇɴᴄᴇ ᴛʜᴀᴛ ɪɴᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇs ʜᴀᴠᴇ ᴏɴ ᴛʜᴇ ᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇ ɪɴ ᴀ ʀᴇɢʀᴇssɪᴏɴ sᴛᴜᴅʏ.
ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ᴀɴᴀʟʏsɪs ᴛᴏᴏʟs ғᴏʀ ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ᴀɴᴀʟʏsɪs
ᴀɴᴀʟʏsɪs ᴏғ ᴠᴀʀɪᴀɴᴄᴇ (ᴀɴᴏᴠᴀ)
ʙʏ ᴡɪʟʟ ᴋᴇɴᴛᴏɴ ʀᴇᴠɪᴇᴡᴇᴅ ʙʏ ᴛᴏʙʏ ᴡᴀʟᴛᴇʀs ᴜᴘᴅᴀᴛᴇᴅ ғᴇʙ ,
ᴡʜᴀᴛ ɪs ᴀɴᴀʟʏsɪs ᴏғ ᴠᴀʀɪᴀɴᴄᴇ (ᴀɴᴏᴠᴀ)?
ᴀɴᴀʟʏsɪs ᴏғ ᴠᴀʀɪᴀɴᴄᴇ (ᴀɴᴏᴠᴀ) ɪs ᴀɴ ᴀɴᴀʟʏsɪs ᴛᴏᴏʟ ᴜsᴇᴅ ɪɴ sᴛᴀᴛɪsᴛɪᴄs ᴛʜᴀᴛ sᴘʟɪᴛs ᴀɴ ᴏʙsᴇʀᴠᴇᴅ ᴀɢɢʀᴇɢᴀᴛᴇ ᴠᴀʀɪᴀʙɪʟɪᴛʏ ғᴏᴜɴᴅ ɪɴsɪᴅᴇ ᴀ ᴅᴀᴛᴀ sᴇᴛ ɪɴᴛᴏ ᴛᴡᴏ ᴘᴀʀᴛs: sʏsᴛᴇᴍᴀᴛɪᴄ ғᴀᴄᴛᴏʀs ᴀɴᴅ ʀᴀɴᴅᴏᴍ ғᴀᴄᴛᴏʀs. ᴛʜᴇ sʏsᴛᴇᴍᴀᴛɪᴄ ғᴀᴄᴛᴏʀs ʜᴀᴠᴇ ᴀ sᴛᴀᴛɪsᴛɪᴄᴀʟ ɪɴғʟᴜᴇɴᴄᴇ ᴏɴ ᴛʜᴇ ɢɪᴠᴇɴ ᴅᴀᴛᴀ sᴇᴛ, ᴡʜɪʟᴇ ᴛʜᴇ ʀᴀɴᴅᴏᴍ ғᴀᴄᴛᴏʀs ᴅᴏ ɴᴏᴛ. ᴀɴᴀʟʏsᴛs ᴜsᴇ ᴛʜᴇ ᴀɴᴏᴠᴀ ᴛᴇsᴛ ᴛᴏ ᴅᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ɪɴғʟᴜᴇɴᴄᴇ ᴛʜᴀᴛ ɪɴᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇs ʜᴀᴠᴇ ᴏɴ ᴛʜᴇ ᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇ ɪɴ ᴀ ʀᴇɢʀᴇssɪᴏɴ sᴛᴜᴅʏ.
ᴛʜᴇ ᴛ- ᴀɴᴅ ᴢ-ᴛᴇsᴛ ᴍᴇᴛʜᴏᴅs ᴅᴇᴠᴇʟᴏᴘᴇᴅ ɪɴ ᴛʜᴇ ᴛʜ ᴄᴇɴᴛᴜʀʏ ᴡᴇʀᴇ ᴜsᴇᴅ ғᴏʀ sᴛᴀᴛɪsᴛɪᴄᴀʟ ᴀɴᴀʟʏsɪs ᴜɴᴛɪʟ , ᴡʜᴇɴ ʀᴏɴᴀʟᴅ ғɪsʜᴇʀ ᴄʀᴇᴀᴛᴇᴅ ᴛʜᴇ ᴀɴᴀʟʏsɪs ᴏғ ᴠᴀʀɪᴀɴᴄᴇ ᴍᴇᴛʜᴏᴅ. ᴀɴᴏᴠᴀ ɪs ᴀʟsᴏ ᴄᴀʟʟᴇᴅ ᴛʜᴇ ғɪsʜᴇʀ ᴀɴᴀʟʏsɪs ᴏғ ᴠᴀʀɪᴀɴᴄᴇ, ᴀɴᴅ ɪᴛ ɪs ᴛʜᴇ ᴇxᴛᴇɴsɪᴏɴ ᴏғ ᴛʜᴇ ᴛ- ᴀɴᴅ ᴢ-ᴛᴇsᴛs. ᴛʜᴇ ᴛᴇʀᴍ ʙᴇᴄᴀᴍᴇ ᴡᴇʟʟ-ᴋɴᴏᴡɴ ɪɴ , ᴀғᴛᴇʀ ᴀᴘᴘᴇᴀʀɪɴɢ ɪɴ ғɪsʜᴇʀ's ʙᴏᴏᴋ, "sᴛᴀᴛɪsᴛɪᴄᴀʟ ᴍᴇᴛʜᴏᴅs ғᴏʀ ʀᴇsᴇᴀʀᴄʜ ᴡᴏʀᴋᴇʀs." ɪᴛ ᴡᴀs ᴇᴍᴘʟᴏʏᴇᴅ ɪɴ ᴇxᴘᴇʀɪᴍᴇɴᴛᴀʟ ᴘsʏᴄʜᴏʟᴏɢʏ ᴀɴᴅ ʟᴀᴛᴇʀ ᴇxᴘᴀɴᴅᴇᴅ ᴛᴏ sᴜʙᴊᴇᴄᴛs ᴛʜᴀᴛ ᴡᴇʀᴇ ᴍᴏʀᴇ ᴄᴏᴍᴘʟᴇx.
ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ғᴏʀ ᴀɴᴏᴠᴀ ɪs:
\ʙᴇɢɪɴ{ᴀʟɪɢɴᴇᴅ} &\ᴛᴇxᴛ{ғ} = \ғʀᴀᴄ{ \ᴛᴇxᴛ{ᴍsᴛ} }{ \ᴛᴇxᴛ{ᴍsᴇ} } \\ &\ᴛᴇxᴛʙғ{ᴡʜᴇʀᴇ:} \\ &\ᴛᴇxᴛ{ғ} = \ᴛᴇxᴛ{ᴀɴᴏᴠᴀ ᴄᴏᴇғғɪᴄɪᴇɴᴛ} \\ &\ᴛᴇxᴛ{ᴍsᴛ} = \ᴛᴇxᴛ{ᴍᴇᴀɴ sᴜᴍ ᴏғ sǫᴜᴀʀᴇs ᴅᴜᴇ ᴛᴏ ᴛʀᴇᴀᴛᴍᴇɴᴛ} \\ &\ᴛᴇxᴛ{ᴍsᴇ} = \ᴛᴇxᴛ{ᴍᴇᴀɴ sᴜᴍ ᴏғ sǫᴜᴀʀᴇs ᴅᴜᴇ ᴛᴏ ᴇʀʀᴏʀ} \\ \ᴇɴᴅ{ᴀʟɪɢɴᴇᴅ}
ғ=
ᴍsᴇ
ᴍsᴛ
ᴡʜᴇʀᴇ:
ғ=ᴀɴᴏᴠᴀ ᴄᴏᴇғғɪᴄɪᴇɴᴛ
ᴍsᴛ=ᴍᴇᴀɴ sᴜᴍ ᴏғ sǫᴜᴀʀᴇs ᴅᴜᴇ ᴛᴏ ᴛʀᴇᴀᴛᴍᴇɴᴛ
ᴍsᴇ=ᴍᴇᴀɴ sᴜᴍ ᴏғ sǫᴜᴀʀᴇs ᴅᴜᴇ ᴛᴏ ᴇʀʀᴏʀ