{"id":45,"date":"2024-05-16T09:09:13","date_gmt":"2024-05-16T09:09:13","guid":{"rendered":"http:\/\/www.ohsumin.com\/sm24_wp\/?p=45"},"modified":"2025-06-11T01:23:00","modified_gmt":"2025-06-11T01:23:00","slug":"%eb%8f%85%eb%a6%bd-t-%ea%b2%80%ec%a0%95","status":"publish","type":"post","link":"http:\/\/www.inmining.co.kr\/?p=45","title":{"rendered":"t-\ubd84\ud3ec(t-distribution)"},"content":{"rendered":"\n
    \n
  1. t-\ubd84\ud3ec \uac1c\uc694<\/a><\/strong><\/li>\n\n\n\n
  2. <\/li>\n<\/ol>\n\n\n\n

    <\/p>\n\n\n\n

    \\(\\)<\/p>\n\n\n\n

    <\/span>t-\ubd84\ud3ec (Student’s t-Distribution) \uac1c\uc694<\/span><\/h3>\n\n\n\n

    t-\ubd84\ud3ec\ub294 \ud1b5\uacc4\ud559\uc5d0\uc11c \uc8fc\ub85c \uc791\uc740 \ud45c\ubcf8 \ud06c\uae30\uc758 \ub370\uc774\ud130\ub97c \ubd84\uc11d\ud560 \ub54c \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \uc774 \ubd84\ud3ec\ub294 \uc815\uaddc \ubd84\ud3ec\uc640 \uc720\uc0ac\ud558\uc9c0\ub9cc, \uaf2c\ub9ac\uac00 \ub354 \ub450\uaebc\uc6cc\uc11c \uadf9\ub2e8\uc801\uc778 \uac12\uc774 \ub098\uc62c \uac00\ub2a5\uc131\uc774 \ub354 \ud07d\ub2c8\ub2e4. \ud45c\ubcf8 \ud06c\uae30\uac00(n>30) \ucee4\uc9c8\uc218\ub85d t-\ubd84\ud3ec\ub294 \uc815\uaddc \ubd84\ud3ec\uc5d0 \uac00\uae4c\uc6cc\uc9d1\ub2c8\ub2e4. t-\ubd84\ud3ec\ub294 \uc8fc\ub85c t-\uac80\uc815(t-test)\uc640 \uc2e0\ub8b0 \uad6c\uac04(CI : Confidence Intervals)\uc744 \uacc4\uc0b0\ud560 \ub54c \uc0ac\uc6a9\ub41c\ub2e4..<\/p>\n\n\n\n

    \uc8fc\uc694 \ud2b9\uc131<\/h4>\n\n\n\n
      \n
    1. \ubaa8\uc591<\/strong>: t-\ubd84\ud3ec\ub294 \ud3c9\uade0\uc774 0\uc774\uace0, \uc911\uc2ec\uc774 \ub300\uce6d\uc801\uc778 \uc885 \ubaa8\uc591\uc744 \uac00\uc9c0\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uaf2c\ub9ac\uac00 \ub450\uaebc\uc6cc\uc11c \uadf9\ub2e8\uac12\uc774 \ubc1c\uc0dd\ud560 \uac00\ub2a5\uc131\uc774 \ub354 \ud07d\ub2c8\ub2e4.<\/li>\n\n\n\n
    2. \uc790\uc720\ub3c4(df : degrees of freedom)<\/strong>: t-\ubd84\ud3ec\uc758 \ubaa8\uc591\uc740 \uc790\uc720\ub3c4\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9d1\ub2c8\ub2e4. \uc790\uc720\ub3c4\uac00 \ucee4\uc9c8\uc218\ub85d \ubd84\ud3ec\ub294 \uc815\uaddc \ubd84\ud3ec\uc5d0 \uac00\uae4c\uc6cc\uc9d1\ub2c8\ub2e4.<\/li>\n\n\n\n
    3. \ud3c9\uade0\uacfc \ubd84\uc0b0<\/strong>:\n
        \n
      • \ud3c9\uade0 : 0<\/li>\n\n\n\n
      • \ubd84\uc0b0 : ( \\( \\frac{\\nu}{\\nu – 2}) (\uc790\uc720\ub3c4 (\\nu > 2) \\))<\/li>\n\n\n\n
      • \\( \\nu = df \\)<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
        \n
        \n
        \"\"<\/figure>\n<\/div>\n\n\n\n
        \n
          \n
        • \\( nu=1 \\)<\/li>\n\n\n\n
        • \\( nu=2 \\)<\/li>\n\n\n\n
        • \\( nu=5 \\)<\/li>\n\n\n\n
        • \\( nu= \\infty \\) <\/li>\n<\/ul>\n<\/div>\n<\/div>\n\n\n\n
          \"\"<\/figure>\n\n\n\n

          <\/span>t-\ubd84\ud3ec vs \uc815\uaddc \ubd84\ud3ec<\/span><\/h3>\n\n\n\n
            \n
          • t-\ubd84\ud3ec\ub294 \uc815\uaddc \ubd84\ud3ec\uc640 \ub2ec\ub9ac \ud45c\ubcf8 \ud06c\uae30\uac00 \uc791\uc740 \uacbd\uc6b0\uc5d0\ub3c4 \uc2e0\ub8b0 \uad6c\uac04\uacfc \uac00\uc124 \uac80\uc815\uc744 \uc218\ud589\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n
          • \ud45c\ubcf8 \ud06c\uae30\uac00 \uc791\uc744\uc218\ub85d(\uc989, \uc790\uc720\ub3c4\uac00 \ub0ae\uc744\uc218\ub85d) t-\ubd84\ud3ec\uc758 \uaf2c\ub9ac\uac00 \ub354 \ub450\uaebc\uc6cc\uc9d1\ub2c8\ub2e4.<\/li>\n\n\n\n
          • <\/li>\n<\/ul>\n\n\n
            \n
            \"\"<\/figure>\n<\/div>\n\n\n

            <\/span>t-\ubd84\ud3ec\uc758 \ud65c\uc6a9 \uc608\uc2dc<\/span><\/h3>\n\n\n\n
              \n
            • t-\uac80\uc815 (t-test)<\/strong>:\n
                \n
              • \ub2e8\uc77c \ud45c\ubcf8 t-\uac80\uc815<\/strong>: \ud45c\ubcf8 \ud3c9\uade0\uc774 \uc54c\ub824\uc9c4 \ubaa8\uc9d1\ub2e8 \ud3c9\uade0\uacfc \ub2e4\ub978\uc9c0 \uc5ec\ubd80\ub97c \uac80\uc815\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n
              • \ub3c5\ub9bd \ud45c\ubcf8 t-\uac80\uc815<\/strong>: \ub450 \uac1c\uc758 \ub3c5\ub9bd\uc801\uc778 \ud45c\ubcf8\uc774 \ub3d9\uc77c\ud55c \ubaa8\uc9d1\ub2e8\uc5d0\uc11c \ub098\uc654\ub294\uc9c0 \uac80\uc815\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n
              • \ub300\uc751 \ud45c\ubcf8 t-\uac80\uc815<\/strong>: \ub3d9\uc77c\ud55c \ud45c\ubcf8\uc5d0\uc11c \ub450 \ubc88 \uce21\uc815\ud55c \uacb0\uacfc\uc758 \ucc28\uc774\ub97c \uac80\uc815\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                  \n
                • \uc2e0\ub8b0 \uad6c\uac04 (Confidence Interval)<\/strong>:\n
                    \n
                  • t-\ubd84\ud3ec\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc791\uc740 \ud45c\ubcf8 \ud06c\uae30\uc5d0 \ub300\ud574 \ud3c9\uade0\uc5d0 \ub300\ud55c \uc2e0\ub8b0 \uad6c\uac04\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                    \"\"<\/figure>\n\n\n\n

                    <\/span>t-\ubd84\ud3ec Python \uc2dc\uac01\ud654<\/span><\/h3>\n\n\n\n

                    \ub2e4\uc74c\uc740 Python \ucf54\ub4dc\ub97c \uc0ac\uc6a9\ud558\uc5ec t-\ubd84\ud3ec\ub97c \uc2dc\uac01\ud654\ud558\ub294 \uc608\uc81c\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n

                    import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.stats import t, norm\n\n# \uc790\uc720\ub3c4 \uc124\uc815\ndf1 = 5\ndf2 = 10\ndf3 = 30\n\n# x \uac12 \uc0dd\uc131\nx = np.linspace(-5, 5, 1000)\n\n# t-\ubd84\ud3ec\uc640 \uc815\uaddc \ubd84\ud3ec \uacc4\uc0b0\ny_t1 = t.pdf(x, df1)\ny_t2 = t.pdf(x, df2)\ny_t3 = t.pdf(x, df3)\ny_norm = norm.pdf(x)\n\n# \ud50c\ub86f \uc0dd\uc131\nplt.figure(figsize=(10, 6))\nplt.plot(x, y_t1, label=f't-distribution (df={df1})')\nplt.plot(x, y_t2, label=f't-distribution (df={df2})')\nplt.plot(x, y_t3, label=f't-distribution (df={df3})')\nplt.plot(x, y_norm, label='Standard Normal Distribution', linestyle='dashed')\n\nplt.title('Comparison of t-Distributions with Normal Distribution')\nplt.xlabel('x')\nplt.ylabel('Probability Density')\nplt.legend()\nplt.grid(True)\nplt.show()<\/code><\/pre>\n\n\n\n
                    \uc774 \ucf54\ub4dc\ub294 \uc790\uc720\ub3c4\uac00 \ub2e4\ub978 t-\ubd84\ud3ec\uc640 \ud45c\uc900 \uc815\uaddc \ubd84\ud3ec\ub97c \ube44\uad50\ud558\uc5ec \uc2dc\uac01\ud654\ud569\ub2c8\ub2e4. \uc774 \uadf8\ub798\ud504\ub97c \ud1b5\ud574 t-\ubd84\ud3ec\uac00 \uc790\uc720\ub3c4\uc5d0 \ub530\ub77c \uc5b4\ub5bb\uac8c \ubcc0\ud654\ud558\ub294\uc9c0, \uadf8\ub9ac\uace0 \uc790\uc720\ub3c4\uac00 \ucee4\uc9c8\uc218\ub85d \uc815\uaddc \ubd84\ud3ec\uc5d0 \uac00\uae4c\uc6cc\uc9c0\ub294\uc9c0\ub97c \ud655\uc778\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n
                    \"\"<\/figure>\n\n\n\n
                    <\/span>t-\ubd84\ud3ec Python \uc2dc\uac01\ud654<\/strong><\/span><\/h3>\n\n\n\n
                      \n
                    • R code snippet to plot the t-distribution (with 1 degree of freedom) <\/li>\n\n\n\n
                    • normal distribution together, with the specified colors<\/li>\n<\/ul>\n\n\n\n
                      # Load necessary library\nlibrary(ggplot2)\n\n# Generate data for plotting\nx <- seq(-5, 5, length.out = 1000)\nnormal_density <- dnorm(x, mean = 0, sd = 1)\nt_density <- dt(x, df = 1)\n\n# Create a data frame\ndata <- data.frame(x = x, normal = normal_density, t_dist = t_density)\n\n# Plot using ggplot2\nggplot(data, aes(x = x)) +\n  geom_line(aes(y = normal, color = \"Normal Distribution (mean=0, sd=1)\"), linetype = \"dashed\") +\n  geom_line(aes(y = t_dist, color = \"t-Distribution (df=1)\")) +\n  scale_color_manual(values = c(\"Normal Distribution (mean=0, sd=1)\" = \"red\", \n                                \"t-Distribution (df=1)\" = \"blue\")) +\n  labs(title = \"Normal Distribution vs t-Distribution (df=1)\",\n       x = \"Value\",\n       y = \"Probability Density\",\n       color = \"Distribution\") +\n  theme_minimal()<\/code><\/pre>\n\n\n\n
                      This code will generate a plot similar to the one created with Python, showing the normal distribution in red and the t-distribution with 1 degree of freedom in blue. You can run this code in any R environment.<\/p>\n","protected":false},"excerpt":{"rendered":"
                      t-\ubd84\ud3ec (Student’s t-Distribution) \uac1c\uc694 t-\ubd84\ud3ec\ub294 \ud1b5\uacc4\ud559\uc5d0\uc11c \uc8fc\ub85c \uc791\uc740 \ud45c\ubcf8 \ud06c\uae30\uc758 \ub370\uc774\ud130\ub97c \ubd84\uc11d\ud560 \ub54c \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \uc774 \ubd84\ud3ec\ub294 \uc815\uaddc \ubd84\ud3ec\uc640…<\/p>\n","protected":false},"author":1,"featured_media":316,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"[]"},"categories":[6],"tags":[19,20,24,23,22,21],"class_list":["post-45","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-stat","tag-t-test","tag-t","tag-24","tag-23","tag-22","tag-21","wpcat-6-id"],"_links":{"self":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/45","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=45"}],"version-history":[{"count":24,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/45\/revisions"}],"predecessor-version":[{"id":630,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/45\/revisions\/630"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/media\/316"}],"wp:attachment":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=45"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=45"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=45"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}