Skip to main content
Global

10.8: Sura ya Mfumo wa Mapitio

  1. Last updated
  2. Save as PDF
  • Page ID
    179664

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    10.1 Kulinganisha Njia mbili za Idadi ya Watu wa kujitegemea

    Hitilafu ya kawaida:\(S E=\sqrt{\frac{\left(s_{1}\right)^{2}}{n_{1}}+\frac{\left(s_{2}\right)^{2}}{n_{2}}}\)

    Takwimu za mtihani (t-score):\(t_{c}=\frac{\left(\overline{x}_{1}-\overline{x}_{2}\right)-\delta_{0}}{\sqrt{\frac{\left(s_{1}\right)^{2}}{n_{1}}+\frac{\left(s_{2}\right)^{2}}{n_{2}}}}\)

    Degrees ya uhuru:
    \(d f=\frac{\left(\frac{\left(s_{1}\right)^{2}}{n_{1}}+\frac{\left(s_{2}\right)^{2}}{n_{2}}\right)^{2}}{\left(\frac{1}{n_{1}-1}\right)\left(\frac{\left(s_{1}\right)^{2}}{n_{1}}\right)^{2}+\left(\frac{1}{n_{2}-1}\right)\left(\frac{\left(s_{2}\right)^{2}}{n_{2}}\right)^{2}}\)

    ambapo:

    \(s_1\)na\(s_2\) ni sampuli kiwango deviations,\(n_1\) na\(n_2\) ni sampuli ukubwa.

    \(\overline{x}_{1}\)na\(\overline{x}_{2}\) ni njia ya sampuli.

    10.2 Viwango vya Cohen kwa Ukubwa mdogo, wa kati, na Ukubwa wa Athari

    Cohen\(d\) ni kipimo cha ukubwa wa athari:

    \(d=\frac{\overline{x}_{1}-\overline{x}_{2}}{s_{\text {pooled}}}\)
    wapi\(s_{\text {pooled}}=\sqrt{\frac{\left(n_{1}-1\right) s_{1}^{2}+\left(n_{2}-1\right) s_{2}^{2}}{n_{1}+n_{2}-2}}\)

    Mtihani wa 10.3 kwa Tofauti katika Njia: Kutokana na tofauti za Idadi ya Watu

    \[t_{c}=\frac{\left(\overline{x}_{1}-\overline{x}_{2}\right)-\delta_{0}}{\sqrt{S^{2}\left(\frac{1}{n_{1}}+\frac{1}{n_{2}}\right)}}\nonumber\]

    \(S_{p}^{2}\)wapi ugomvi wa pamoja uliotolewa na formula:

    \[S_{p}^{2}=\frac{\left(n_{1}-1\right) s_{2}^{1}+\left(n_{2}-1\right) s_{2}^{2}}{n_{1}+n_{2}-2}\nonumber\]

    10.4 Kulinganisha Idadi ya Watu wa Independent mbili

    Uwiano uliochanganywa:\(p_{c}=\frac{x_{A}+x_{B}}{n_{A}+n_{B}}\)

    Takwimu za mtihani (z-alama):\(Z_{c}=\frac{\left(p^{\prime}_{A}-p^{\prime}_{B}\right)}{\sqrt{p_{c}\left(1-p_{c}\right)\left(\frac{1}{n_{A}}+\frac{1}{n_{B}}\right)}}\)

    wapi

    \(p_{A}^{\prime}\)na\(p_{B}^{\prime}\) ni idadi ya sampuli,\(p_A\) na\(p_B\) ni idadi ya watu,

    \(P_c\)ni idadi ya pamoja,\(n_A\) na\(n_B\) ni ukubwa sampuli.

    10.5 Idadi ya Watu Maana na Mapungufu ya Kiwango Kinachojulikana

    Takwimu za mtihani (z-alama):

    \(Z_{c}=\frac{\left(\overline{x}_{1}-\overline{x}_{2}\right)-\delta_{0}}{\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}}\)

    ambapo:
    \(\sigma_1\) na\(\sigma_2\) ni maalumu idadi ya watu kiwango deviations. \(n_1\)na\(n_2\) ni ukubwa wa sampuli. \(\overline{x}_{1}\)na\(\overline{x}_{2}\) ni njia ya sampuli. \(\mu_1\)na\(\mu_2\) ni maana ya idadi ya watu.

    10.6 Sampuli zinazofanana au zilizounganishwa

    Takwimu za mtihani (t-alama):\(t_{c}=\frac{\overline{x}_{d}-\mu_{d}}{\left(\frac{s_{d}}{\sqrt{n}}\right)}\)

    ambapo:

    \(\overline{x}_{d}\)ni maana ya tofauti za sampuli. \(\mu_d\)ni maana ya tofauti ya idadi ya watu. \(s_d\)ni sampuli kiwango kupotoka ya tofauti. \(n\)ni ukubwa wa sampuli.