Liforomo tsa Lipalo-palo Patlisisong
Lipalopalo ke lekala la lipalo le amehang ka pokello, tlhahlobo, tlhaloso le nehelano ea lintlha. Patlisisong, ebang ke ea mahlale, boenjiniere, mahlale a sechaba, kapa esita le ea botho, lipalo-palo li bapala karolo ea bohlokoa ho thuseng bafuputsi ho leka likhopolo-taba, ho etsa likhakanyo le ho etsa liqeto. Sengoloa sena se tla tšohla mekhoa e meng ea motheo ea lipalo-palo le ts'ebeliso ea tsona lipatlisisong.
1. Lipalopalo tse Hlalosang
Lipalopalo tse hlalosang li sebelisoa ho hlalosa lintlha tse bokelletsoeng thutong. Li kenyelletsa litekanyo tse fapaneng tse fanang ka kakaretso ea lintlha.
a. Karolelano (Karolelano)
Boleng bo tloaelehileng ke boleng bo sebelisoang haholo lipalo-palong. Ke kakaretso ea boleng bohle ba dataset bo arotsoeng ka palo ea boleng.
\[ \text{Mean} (\bar{x}) = \frac{\sum_{i=1}^{n} x_i}{n} \]
Di mana:
– \( \sum \) ke letšoao la kakaretso, le bolelang ho kopanya boleng bohle ba \( x \) ho tloha ho 1 ho isa ho \( n \).
– \( x_i \) ke boleng bo bong le bo bong bo ho sete ya data.
– \( n \) ke palo yohle ya boleng bo ho dataset.
b. Bohareng
Bohare ke boleng bo bohareng ho sete ya data e hlophisitsweng. Haeba palo ya boleng ho data e sa tlwaeleha, bohare ke boleng bo bohareng. Haeba palo ya boleng e lekana, bohare ke karolelano ya boleng bo bohareng bo le bong.
c. Mokhoa
Mokhoa ke boleng bo hlahang khafetsa ho sete ea data. Sete ea data e ka ba le mokhoa o le mong (unimodal), mekhoa e fetang e le 'ngoe (multimodal), kapa ha e na mokhoa ho hang.
d. Sebaka
Bophara ke phapang pakeng tsa boleng bo phahameng le bo tlase ho sete ea data.
\[ \text{Range} = \text{Max}(x) – \text{Min}(x) \]
e. Ho kheloha ho tloaelehileng
Ho kheloha ho tloaelehileng ke tekanyo ea ho ata kapa ho hasana ha data ho potoloha karolelano. Foromo ea ho kheloha ho tloaelehileng ha baahi ke:
\[ \sigma = \sqrt{\frac{\sum_{i=1}^{N} (x_i – \mu)^2}{N}} \]
Le bakeng sa mohlala:
\[ s = \sqrt{\frac{\sum_{i=1}^{n} (x_i – \bar{x})^2}{n-1}} \]
Di mana:
– \( \sigma \) ke phapang e tloaelehileng ea baahi.
– \( s \) ke mohlala wa ho kheloha ho tloaelehileng.
– \( x_i \) ke boleng bo bong le bo bong bo ho sete ya data.
– \( \mu \) ke karolelano ya baahi.
– \( \bar{x} \) ke karolelano ya mohlala.
– \( N \) ke palo yohle ya boleng baahing.
– \( n \) ke palo yohle ya boleng ba sampole.
2. Lipalopalo tsa ho Qetela
Lipalopalo tsa ho nahana li lumella bafuputsi ho etsa liqeto ka baahi ho latela sampole ea data. E akaretsa mekhoa e fapaneng, joalo ka teko ea khopolo-taba, ho khutlela morao le tlhahlobo ea phapang (ANOVA).
a. Teko ea Khopolo-taba
Teko ea khopolo-taba ke mokhoa oa lipalo-palo o sebelisoang ho fumana hore na ho na le bopaki bo lekaneng sampole ea data ho fihlela qeto ea hore boemo bo teng sechabeng.
i. Khopolo-taba e se nang thuso (H0) le Khopolo-taba e 'Ngoe (H1)
– Null Hypothesis (H0): Ha ho na phapang kapa phello.
– Khopolo-taba e 'Ngoe (H1): Ho na le phapang kapa phello.
Teko e etsoa ho sebelisoa lipalo-palo tsa teko, joalo ka teko ea t, teko ea chi-square, kapa ANOVA, 'me ho bapisoa boleng ba p le boemo ba bohlokoa (\(\alpha\)), hangata 0,05.
ii. teko ea t
Teko ea t e sebelisoa ho bapisa mekhoa ea lihlopha tse peli. Ho na le mefuta e 'maloa ea teko ea t, joalo ka lisampole tse ikemetseng tsa teko ea t le teko ea t e kopantsoeng.
Foromo ea motheo bakeng sa teko ea t bakeng sa lisampole tse ikemetseng ke:
\[ t = \frac{\bar{x}_1 – \bar{x}_2}{\sqrt{\left( \frac{s_1^2}{n_1} \right) + \left( \frac{s_2^2}{n_2} \right)}} \]
b. Ho kgutlela morao
Ho khutlela morao ho sebediswa ho etsa mohlala wa kamano pakeng tsa diphetoho tse ikemetseng tse le nngwe kapa tse ngata (diponelopele) le phetoho e itshetlehileng (karabo).
i. Ho Fokotsa ho Bonolo ha Mola o Molele
Mehlala e bonolo ea ho khutlela morao e bonts'a kamano pakeng tsa phetoho e le 'ngoe e ikemetseng le phetoho e le 'ngoe e itšetlehileng ka eona.
Tekanyo e bonolo ea ho khutlela morao ka mola ke:
\[ y = \beta_0 + \beta_1 x + \epsilon \]
Di mana:
– \( y \) ke phetoho e itshetlehileng.
– \( x \) ke phetoho e ikemetseng.
– \( \beta_0 \) ke thibelo.
– \( \beta_1 \) ke coefficient ya regression.
– \( \epsilon \) ke phoso.
ii. Ho Fokotsa Methapo e Mengata
Mehlala e mengata ea ho khutlela morao e nang le mola o le mong e bontša kamano pakeng tsa mefuta e mengata e ikemetseng le mofuta o le mong o itšetlehileng ka oona.
Tekanyo ea ho khutlela morao ka mola o le mong ke:
\[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots + \beta_p x_p + \epsilon \]
Di mana:
– \( y \) ke phetoho e itshetlehileng.
– \( x_1, x_2, \ldots, x_p \) ke phetoho e ikemetseng.
– \( \beta_0 \) ke thibelo.
– \( \beta_p \) ke coefficient ya regression bakeng sa phetoho e ikemetseng \( p \).
– \( \epsilon \) ke phoso.
c. Tlhahlobo ea Phapang (ANOVA)
ANOVA e sebediswa ho bapisa mekgwa ya dihlopha tse tharo kapa ho feta. ANOVA e fumana hore na ho na le phapang e kgolo pakeng tsa mekgwa ya dihlopha ka ho bapisa phapang pakeng tsa dihlopha le phapang e ka hare ho dihlopha.
Foromo ea motheo ea ANOVA ke:
\[ F = \frac{\text{Between-Group Variability}}{\text{Within-Group Variability}} \]
Palo-palo ea F e baloa le ho bapisoa le boleng ba bohlokoa ba kabo ea F ho fumana hore na ho na le phapang e kholo lipakeng tsa meelelo ea sehlopha.
3. Kamano
Kamano e lekanya matla le tataiso ea kamano e otlolohileng pakeng tsa mefuta e 'meli e fapaneng.
a. Koefficient ea Kamano ea Pearson (r)
Tekanyo ea kamano ea Pearson ke tekanyo e sebelisoang haholo ho lekanya kamano e otlolohileng lipakeng tsa li-variable tse peli.
Foromo ea coefficient ea kamano ea Pearson ke:
\[ r = \frac{\sum_{i=1}^{n} (x_i – \bar{x})(y_i – \bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i – \bar{x})^2} \sqrt{\sum_{i=1}^{n} (y_i – \bar{y})^2}} \]
Di mana:
– \( r \) ke coefficient ya kamano ya Pearson.
– \( x_i \) le \( y_i \) ke boleng ba di-variable tse pedi.
– \( \bar{x} \) le \( \bar{y} \) ke karolelano ya diphetoho tse pedi.
Boleng ba \( r \) bo tloha ho -1 (kamano e nepahetseng e mpe) ho isa ho +1 (kamano e ntle e phethahetseng), mme 0 e bontsha hore ha ho na kamano.
Ho koala
Lipalopalo ke sesebelisoa sa bohlokoa sa lipatlisiso se thusang bafuputsi ho hlahisa, ho sekaseka le ho etsa liqeto ho tsoa ho data. Sengoloa sena se akaretsa mekhoa e 'maloa feela ea motheo ea lipalo-palo tse hlalosang le tse hakanyang, hammoho le kamano. Le hoja ho le bonolo, kutloisiso e felletseng ea mekhoa ena ke ea bohlokoa bakeng sa ho etsa litlhahlobo tse nepahetseng le ho etsa liqeto tse nepahetseng ho tsoa ho data ea lipatlisiso. Ka ho tseba lipalo-palo hantle, bafuputsi ba ka netefatsa hore liphuputso tsa bona li thehiloe tlhahlobong e tiileng le e tšepahalang.
