{"id":21649,"date":"2026-08-03T17:13:17","date_gmt":"2026-08-03T11:43:17","guid":{"rendered":"https:\/\/www.geographynotespdf.com\/?p=21649"},"modified":"2026-10-09T22:47:44","modified_gmt":"2026-10-09T17:17:44","slug":"complete-analysis-of-variance","status":"publish","type":"post","link":"https:\/\/geographynotespdf.com\/cms\/complete-analysis-of-variance\/","title":{"rendered":"16. Complete Analysis of Variance (ANOVA) – \u0935\u093f\u091a\u0930\u0923 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u0964 Easy Explanation 2026"},"content":{"rendered":"\n\n\n
\n

Analysis of Variance (ANOVA) <\/span><\/strong><\/h2>\n

– \u0935\u093f\u091a\u0930\u0923 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

\"Analysis<\/p>\n

\u092a\u0930\u093f\u091a\u092f <\/span><\/strong><\/span><\/p>\n

(Introduction)<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 Analysis of Variance (ANOVA) \u092f\u093e \u0935\u093f\u091a\u0930\u0923 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093e\u092e\u093f\u0924\u0940\u092f (Parametric) \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0939\u0948, \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0924\u0940\u0928 \u092f\u093e \u0924\u0940\u0928 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0938\u092e\u0942\u0939\u094b\u0902 (Groups) \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u094b\u0902 (Means) \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 <\/span><\/p>\n

\u00a0 \u00a0 \u00a0ANOVA \u0915\u093e \u0935\u093f\u0915\u093e\u0938 \u092a\u094d\u0930\u0938\u093f\u0926\u094d\u0927 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u0935\u093f\u0926\u094d Sir Ronald A. Fisher (1925) \u0928\u0947 \u0915\u093f\u092f\u093e \u0925\u093e, \u0907\u0938\u0932\u093f\u090f \u0907\u0938\u0947 F-Test \u092d\u0940 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

\u00a0 \u00a0 ANOVA \u0915\u093e \u092e\u0941\u0916\u094d\u092f \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u093e \u0939\u0948 \u0915\u093f \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u092a\u093e\u092f\u093e \u0917\u092f\u093e \u0905\u0902\u0924\u0930 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 (Significant) \u0939\u0948 \u092f\u093e \u0915\u0947\u0935\u0932 \u0938\u0902\u092f\u094b\u0917 (Random Chance) \u0915\u0947 \u0915\u093e\u0930\u0923 \u0939\u0948\u0964<\/span><\/p>\n

\u092a\u0930\u093f\u092d\u093e\u0937\u093e (Definition)<\/span><\/strong><\/span><\/p>\n

Ronald A. Fisher \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930,<\/span><\/strong><\/p>\n

\u00a0 \u00a0 “Analysis of Variance is a statistical technique used to test whether the means of three or more populations are equal.”<\/span><\/p>\n

\u00a0 \u00a0\u0905\u0930\u094d\u0925\u093e\u0924\u094d ANOVA \u090f\u0915 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u0924\u0915\u0928\u0940\u0915 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u0924\u0940\u0928 \u092f\u093e \u0924\u0940\u0928 \u0938\u0947 \u0905\u0927\u093f\u0915 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u094b\u0902 \u0915\u0940 \u0938\u092e\u093e\u0928\u0924\u093e \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

ANOVA \u0915\u093e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f <\/span><\/strong><\/span><\/p>\n

(Objectives of ANOVA)<\/span><\/strong><\/span><\/p>\n

1. \u0924\u0940\u0928 \u092f\u093e \u0905\u0927\u093f\u0915 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

2. \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0905\u0902\u0924\u0930 \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u0928\u093e\u0964<\/span><\/p>\n

3. \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e (Hypothesis) \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

4. \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0915\u093e\u0930\u0915\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u092d\u093e\u0935 \u0915\u093e \u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928 \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

5. \u0905\u0928\u0941\u0938\u0902\u0927\u093e\u0928 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937\u094b\u0902 \u0915\u0940 \u0935\u0948\u091c\u094d\u091e\u093e\u0928\u093f\u0915 \u092a\u0941\u0937\u094d\u091f\u093f \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

6. \u0915\u0943\u0937\u093f, \u092d\u0942\u0917\u094b\u0932, \u0938\u092e\u093e\u091c\u0936\u093e\u0938\u094d\u0924\u094d\u0930, \u091a\u093f\u0915\u093f\u0924\u094d\u0938\u093e \u090f\u0935\u0902 \u0936\u093f\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

ANOVA \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 <\/span><\/strong><\/span><\/p>\n

(Principle of ANOVA)<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 ANOVA \u0907\u0938 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u0939\u0948 \u0915\u093f \u0915\u0941\u0932 \u0935\u093f\u091a\u0930\u0923 (Total Variance) \u0915\u094b \u0926\u094b \u092d\u093e\u0917\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948-<\/span><\/p>\n

1. \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0935\u093f\u091a\u0930\u0923 (Between Group Variance)<\/span><\/p>\n

2. \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0915\u093e \u0935\u093f\u091a\u0930\u0923 (Within Group Variance)<\/span><\/p>\n

\u00a0 \u00a0 \u092f\u0926\u093f \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0935\u093f\u091a\u0930\u0923, \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0915\u0947 \u0935\u093f\u091a\u0930\u0923 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0905\u0927\u093f\u0915 \u0939\u0948, \u0924\u094b \u092f\u0939 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0905\u0902\u0924\u0930 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0964<\/span><\/p>\n

ANOVA \u0915\u093e \u0938\u0942\u0924\u094d\u0930 (Formula)<\/span><\/h1>\n

F = Mean Square Between Groups (MSB)\/Mean Square Within Groups (MSW)<\/span><\/p>\n

\u091c\u0939\u093e\u0901-<\/span><\/p>\n

F = F-Statistic<\/span><\/p>\n

MSB = \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0914\u0938\u0924 \u0935\u093f\u091a\u0930\u0923<\/span><\/p>\n

MSW = \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0915\u093e \u0914\u0938\u0924 \u0935\u093f\u091a\u0930\u0923<\/span><\/p>\n

ANOVA \u0915\u0940 \u092e\u0942\u0932 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e\u090f\u0901 (Assumptions)<\/span><\/strong><\/h3>\n

✍️ <\/span><\/span>\u0921\u0947\u091f\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 (Normal Distribution) \u0915\u093e \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0938\u092d\u0940 \u0938\u092e\u0942\u0939 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 (Independent) \u0939\u094b\u0928\u0947 \u091a\u093e\u0939\u093f\u090f\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u093e \u0935\u093f\u091a\u0930\u0923 \u0938\u092e\u093e\u0928 (Homogeneity of Variance) \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0921\u0947\u091f\u093e \u0905\u0902\u0924\u0930\u093e\u0932 (Interval) \u092f\u093e \u0905\u0928\u0941\u092a\u093e\u0924 (Ratio) \u092e\u093e\u092a \u0938\u094d\u0924\u0930 \u0915\u093e \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0928\u092e\u0942\u0928\u0947 \u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 (Random Sampling) \u0939\u094b\u0928\u0947 \u091a\u093e\u0939\u093f\u090f\u0964<\/span><\/p>\n

ANOVA \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930 <\/span><\/span><\/strong><\/span><\/p>\n

(Types of ANOVA)<\/span><\/span><\/strong><\/span><\/p>\n

(\u0915) One-Way ANOVA <\/span><\/strong><\/span><\/p>\n

(\u090f\u0915-\u092e\u093e\u0930\u094d\u0917\u0940\u092f ANOVA):<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u091c\u092c \u0915\u0947\u0935\u0932 \u090f\u0915 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930 (One Independent Variable) \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0924\u0940\u0928 \u092f\u093e \u0905\u0927\u093f\u0915 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u094b\u0902 (Means) \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u0924\u092c One-Way ANOVA \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 <\/span><\/p>\n

\u00a0 \u00a0 \u0907\u0938\u092e\u0947\u0902 \u092f\u0939 \u091c\u093e\u0901\u091a\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f \u0938\u092e\u093e\u0928 \u0939\u0948\u0902 \u092f\u093e \u0909\u0928\u092e\u0947\u0902 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0902\u0924\u0930 \u0939\u0948\u0964<\/span><\/p>\n

\u0909\u0926\u093e\u0939\u0930\u0923: \u090f\u0915 \u0936\u094b\u0927\u0915\u0930\u094d\u0924\u093e \u092f\u0939 \u091c\u093e\u0928\u0928\u093e \u091a\u093e\u0939\u0924\u093e \u0939\u0948 \u0915\u093f \u092c\u093f\u0939\u093e\u0930, \u0909\u0924\u094d\u0924\u0930 \u092a\u094d\u0930\u0926\u0947\u0936 \u090f\u0935\u0902 \u091d\u093e\u0930\u0916\u0902\u0921 \u092e\u0947\u0902 \u0927\u093e\u0928 \u0915\u0940 \u0914\u0938\u0924 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e (Quintal\/Hectare) \u092e\u0947\u0902 \u0915\u094b\u0908 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0902\u0924\u0930 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902\u0964<\/span><\/p>\n

\u092f\u0939\u093e\u0901-<\/span><\/p>\n

\u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930 (Independent Variable) = \u0930\u093e\u091c\u094d\u092f (3 \u0938\u092e\u0942\u0939)<\/span><\/p>\n

\u0906\u0936\u094d\u0930\u093f\u0924 \u091a\u0930 (Dependent Variable) = \u0927\u093e\u0928 \u0915\u0940 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e<\/span><\/p>\n

\u00a0 \u00a0\u092f\u0926\u093f ANOVA \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u0938\u093e\u0930\u094d\u0925\u0915 (Significant) \u0906\u0924\u093e \u0939\u0948, \u0924\u094b \u092f\u0939 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e\u090f\u0917\u093e \u0915\u093f \u0915\u092e-\u0938\u0947-\u0915\u092e \u090f\u0915 \u0930\u093e\u091c\u094d\u092f \u0915\u0940 \u0914\u0938\u0924 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e \u0905\u0928\u094d\u092f \u0930\u093e\u091c\u094d\u092f\u094b\u0902 \u0938\u0947 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964<\/span><\/p>\n

(\u0916) Two-Way ANOVA<\/span><\/strong><\/span><\/p>\n

(\u0926\u094b-\u092e\u093e\u0930\u094d\u0917\u0940\u092f ANOVA):<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u091c\u092c \u0926\u094b \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930\u094b\u0902 (Two Independent Variables) \u0915\u093e \u090f\u0915 \u0906\u0936\u094d\u0930\u093f\u0924 \u091a\u0930 (Dependent Variable) \u092a\u0930 \u0938\u0902\u092f\u0941\u0915\u094d\u0924 (Combined) \u090f\u0935\u0902 \u092a\u0943\u0925\u0915 (Individual) \u092a\u094d\u0930\u092d\u093e\u0935 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e \u0939\u094b, \u0924\u092c Two-Way ANOVA \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

\u00a0 \u00a0 \u092f\u0939 \u0915\u0947\u0935\u0932 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u093e\u0930\u0915 \u0915\u0947 \u092a\u094d\u0930\u092d\u093e\u0935 \u0915\u093e \u0939\u0940 \u0928\u0939\u0940\u0902, \u092c\u0932\u094d\u0915\u093f \u092f\u0939 \u092d\u0940 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094d\u092f\u093e \u0926\u094b\u0928\u094b\u0902 \u0915\u093e\u0930\u0915 \u092e\u093f\u0932\u0915\u0930 (Interaction Effect) \u092d\u0940 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n

\u0909\u0926\u093e\u0939\u0930\u0923:<\/span>\u00a0\u090f\u0915 \u0936\u094b\u0927\u0915\u0930\u094d\u0924\u093e \u092f\u0939 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u0930\u094d\u0937\u093e (Rainfall) \u0924\u0925\u093e \u0909\u0930\u094d\u0935\u0930\u0915 (Fertilizer) \u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u0917\u0947\u0939\u0942\u0901 \u0909\u0924\u094d\u092a\u093e\u0926\u0928 \u092a\u0930 \u0915\u094d\u092f\u093e \u092a\u094d\u0930\u092d\u093e\u0935 \u092a\u0921\u093c\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

\u092f\u0939\u093e\u0901-<\/span><\/p>\n

\u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930-1 = \u0935\u0930\u094d\u0937\u093e (\u0915\u092e, \u092e\u0927\u094d\u092f\u092e, \u0905\u0927\u093f\u0915)<\/span><\/p>\n

\u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930-2 = \u0909\u0930\u094d\u0935\u0930\u0915 (\u0915\u092e, \u092e\u0927\u094d\u092f\u092e, \u0905\u0927\u093f\u0915)<\/span><\/p>\n

\u0906\u0936\u094d\u0930\u093f\u0924 \u091a\u0930 = \u0917\u0947\u0939\u0942\u0901 \u0909\u0924\u094d\u092a\u093e\u0926\u0928 (\u0915\u094d\u0935\u093f\u0902\u091f\u0932\/\u0939\u0947\u0915\u094d\u091f\u0947\u092f\u0930)<\/span><\/p>\n

Two-Way ANOVA \u0938\u0947 \u0928\u093f\u092e\u094d\u0928 \u0924\u0940\u0928 \u092c\u093e\u0924\u0947\u0902 \u091c\u094d\u091e\u093e\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902-<\/span><\/p>\n

1. \u0915\u0947\u0935\u0932 \u0935\u0930\u094d\u0937\u093e \u0915\u093e \u092a\u094d\u0930\u092d\u093e\u0935\u0964<\/span><\/p>\n

2. \u0915\u0947\u0935\u0932 \u0909\u0930\u094d\u0935\u0930\u0915 \u0915\u093e \u092a\u094d\u0930\u092d\u093e\u0935\u0964<\/span><\/p>\n

3. \u0935\u0930\u094d\u0937\u093e \u090f\u0935\u0902 \u0909\u0930\u094d\u0935\u0930\u0915 \u0915\u0947 \u0938\u0902\u092f\u0941\u0915\u094d\u0924 (Interaction) \u092a\u094d\u0930\u092d\u093e\u0935 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u0964<\/span><\/p>\n

(\u0917) Repeated Measures ANOVA <\/span><\/strong><\/span><\/p>\n

(\u092a\u0941\u0928\u0930\u093e\u0935\u0943\u0924\u094d\u0924 \u092e\u093e\u092a\u0928 ANOVA):<\/span><\/strong><\/span><\/p>\n

\u00a0 \u091c\u092c \u090f\u0915 \u0939\u0940 \u0938\u092e\u0942\u0939 (Same Group) \u0915\u094b \u0905\u0932\u0917-\u0905\u0932\u0917 \u0938\u092e\u092f (Different Time) \u092f\u093e \u0905\u0932\u0917-\u0905\u0932\u0917 \u092a\u0930\u093f\u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 (Different Conditions) \u092e\u0947\u0902 \u092c\u093e\u0930-\u092c\u093e\u0930 \u092e\u093e\u092a\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u092c Repeated Measures ANOVA \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

\u00a0 \u00a0 \u0907\u0938\u092e\u0947\u0902 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0938\u092e\u0942\u0939 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0947, \u092c\u0932\u094d\u0915\u093f \u090f\u0915 \u0939\u0940 \u0938\u092e\u0942\u0939 \u0915\u093e \u092c\u093e\u0930-\u092c\u093e\u0930 \u0905\u0935\u0932\u094b\u0915\u0928 (Repeated Observation) \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

\u0909\u0926\u093e\u0939\u0930\u0923: <\/span>\u090f\u0915 \u0936\u094b\u0927\u0915\u0930\u094d\u0924\u093e \u092a\u091f\u0928\u093e \u091c\u093f\u0932\u0947 \u0915\u0940 \u0914\u0938\u0924 \u0935\u093e\u0930\u094d\u0937\u093f\u0915 \u0935\u0930\u094d\u0937\u093e \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 2020, 2022 \u090f\u0935\u0902 2024 \u092e\u0947\u0902 \u0915\u0930\u0924\u093e \u0939\u0948 \u0914\u0930 \u092f\u0939 \u091c\u093e\u0928\u0928\u093e \u091a\u093e\u0939\u0924\u093e \u0939\u0948 \u0915\u093f \u0907\u0928 \u0935\u0930\u094d\u0937\u094b\u0902 \u092e\u0947\u0902 \u0935\u0930\u094d\u0937\u093e \u092e\u0947\u0902 \u0915\u094b\u0908 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0939\u0941\u0906 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902\u0964<\/span><\/p>\n

\u092f\u0939\u093e\u0901-<\/span><\/p>\n

\u0938\u092e\u0942\u0939 = \u090f\u0915 \u0939\u0940 \u091c\u093f\u0932\u093e (\u092a\u091f\u0928\u093e)<\/span><\/p>\n

\u0938\u092e\u092f = 2020, 2022 \u090f\u0935\u0902 2024<\/span><\/p>\n

\u0906\u0936\u094d\u0930\u093f\u0924 \u091a\u0930 = \u0914\u0938\u0924 \u0935\u093e\u0930\u094d\u0937\u093f\u0915 \u0935\u0930\u094d\u0937\u093e<\/span><\/p>\n

\u00a0 \u00a0\u092f\u0926\u093f ANOVA \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u0938\u093e\u0930\u094d\u0925\u0915 \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e\u090f\u0917\u093e \u0915\u093f \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0935\u0930\u094d\u0937\u094b\u0902 \u092e\u0947\u0902 \u0935\u0930\u094d\u0937\u093e \u092e\u0947\u0902 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0939\u0941\u0906 \u0939\u0948\u0964<\/span><\/p>\n

\u0924\u0940\u0928\u094b\u0902 ANOVA \u0915\u093e \u0905\u0902\u0924\u0930 (Difference between Types of ANOVA)<\/span><\/strong><\/span><\/p>\n\n\n\n\n\n\n\n
\u0906\u0927\u093e\u0930<\/span><\/td>\nOne-Way ANOVA<\/span><\/td>\nTwo-Way ANOVA<\/span><\/td>\nRepeated Measures ANOVA<\/span><\/td>\n<\/tr>\n
\u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930<\/span><\/td>\n1<\/span><\/td>\n2<\/span><\/td>\n\u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903 1 (\u0938\u092e\u092f\/\u0938\u094d\u0925\u093f\u0924\u093f)<\/span><\/td>\n<\/tr>\n
\u0938\u092e\u0942\u0939<\/span><\/td>\n\u0905\u0932\u0917-\u0905\u0932\u0917 \u0938\u092e\u0942\u0939<\/span><\/td>\n\u0905\u0932\u0917-\u0905\u0932\u0917 \u0938\u092e\u0942\u0939<\/span><\/td>\n\u090f\u0915 \u0939\u0940 \u0938\u092e\u0942\u0939<\/span><\/td>\n<\/tr>\n
\u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/span><\/td>\n\u0924\u0940\u0928 \u092f\u093e \u0905\u0927\u093f\u0915 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e<\/span><\/td>\n\u0926\u094b \u0915\u093e\u0930\u0915\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u092d\u093e\u0935 \u090f\u0935\u0902 \u0909\u0928\u0915\u0947 \u0938\u0902\u092f\u0941\u0915\u094d\u0924 \u092a\u094d\u0930\u092d\u093e\u0935 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928<\/span><\/td>\n\u090f\u0915 \u0939\u0940 \u0938\u092e\u0942\u0939 \u092e\u0947\u0902 \u0938\u092e\u092f \u092f\u093e \u092a\u0930\u093f\u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928<\/span><\/td>\n<\/tr>\n
\u0909\u0926\u093e\u0939\u0930\u0923<\/span><\/td>\n\u092c\u093f\u0939\u093e\u0930, \u092f\u0942\u092a\u0940 \u090f\u0935\u0902 \u091d\u093e\u0930\u0916\u0902\u0921 \u0915\u0940 \u0927\u093e\u0928 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e<\/span><\/td>\n\u0935\u0930\u094d\u0937\u093e \u090f\u0935\u0902 \u0909\u0930\u094d\u0935\u0930\u0915 \u0915\u093e \u0917\u0947\u0939\u0942\u0901 \u0909\u0924\u094d\u092a\u093e\u0926\u0928 \u092a\u0930 \u092a\u094d\u0930\u092d\u093e\u0935<\/span><\/td>\n\n

2020, 2022 \u090f\u0935\u0902 2024 \u092e\u0947\u0902 \u090f\u0915 \u0939\u0940 \u091c\u093f\u0932\u0947 \u0915\u0940 \u0935\u0930\u094d\u0937\u093e \u0915\u0940 \u0924\u0941\u0932\u0928\u093e<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

ANOVA \u0915\u0930\u0928\u0947 \u0915\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e (Steps of ANOVA)<\/span><\/strong><\/span><\/p>\n

1. \u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e (H\u2080) \u090f\u0935\u0902 \u0935\u0948\u0915\u0932\u094d\u092a\u093f\u0915 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e (H\u2081) \u092c\u0928\u093e\u0928\u093e\u0964<\/span><\/p>\n

2. \u092e\u0939\u0924\u094d\u0935 \u0938\u094d\u0924\u0930 (Significance Level, \u03b1 = 0.05) \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

3. Sum of Squares (SS) \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

4. Degree of Freedom (df) \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

5. Mean Square (MS) \u0928\u093f\u0915\u093e\u0932\u0928\u093e\u0964<\/span><\/p>\n

6. F-\u092e\u0942\u0932\u094d\u092f \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

7. F-Table \u0938\u0947 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u093e\u0964<\/span><\/p>\n

8. \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u0928\u093e\u0964<\/span><\/p>\n

ANOVA \u0938\u093e\u0930\u0923\u0940 (ANOVA Table)<\/span><\/strong><\/span><\/p>\n\n\n\n\n\n\n
\u0938\u094d\u0930\u094b\u0924<\/span><\/td>\nSS<\/span><\/td>\ndf<\/span><\/td>\nMS<\/span><\/td>\nF<\/span><\/td>\n<\/tr>\n
\u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a (Between Groups)<\/span><\/td>\nSSB<\/span><\/td>\nk\u22121<\/span><\/td>\nMSB<\/span><\/td>\nF = MSB\/MSW<\/span><\/td>\n<\/tr>\n
\u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092d\u0940\u0924\u0930 (Within Groups)<\/span><\/td>\nSSW<\/span><\/td>\nN\u2212k<\/span><\/td>\nMSW<\/span><\/td>\n<\/td>\n<\/tr>\n
\u0915\u0941\u0932 (Total)<\/span><\/td>\nSST<\/span><\/td>\nN\u22121<\/span><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u092d\u0942\u0917\u094b\u0932 \u092e\u0947\u0902 ANOVA \u0915\u0947 \u0909\u092a\u092f\u094b\u0917 <\/span><\/strong><\/span><\/h3>\n

(Applications in Geography)<\/span><\/strong><\/span><\/h3>\n

✍️ <\/span><\/span>\u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0930\u093e\u091c\u094d\u092f\u094b\u0902 \u0915\u0940 \u0935\u0930\u094d\u0937\u093e \u0915\u0940 \u0924\u0941\u0932\u0928\u093e\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u091c\u093f\u0932\u094b\u0902 \u0915\u0940 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0918\u0928\u0924\u094d\u0935 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u092d\u0942\u092e\u093f \u0909\u092a\u092f\u094b\u0917 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u094b\u0902 \u0915\u0940 \u0915\u0943\u0937\u093f \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e \u0915\u0940 \u0924\u0941\u0932\u0928\u093e\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u091c\u0932 \u0917\u0941\u0923\u0935\u0924\u094d\u0924\u093e \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u0940\u092f \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u091c\u0932\u0935\u093e\u092f\u0941 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u092a\u094d\u0930\u092d\u093e\u0935\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u092e\u093f\u091f\u094d\u091f\u0940 \u0915\u0940 \u0909\u0930\u094d\u0935\u0930\u0924\u093e \u0915\u0940 \u0924\u0941\u0932\u0928\u093e\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u0940\u092f \u0935\u093f\u0915\u093e\u0938 \u0938\u094d\u0924\u0930 \u0915\u093e \u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928\u0964<\/span><\/p>\n

ANOVA \u0915\u0947 \u0932\u093e\u092d (Advantages)<\/span><\/strong><\/span><\/h3>\n

✍️ <\/span><\/span>\u0924\u0940\u0928 \u092f\u093e \u0905\u0927\u093f\u0915 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u090f\u0915 \u0938\u093e\u0925 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0938\u092e\u092f \u090f\u0935\u0902 \u0936\u094d\u0930\u092e \u0915\u0940 \u092c\u091a\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

✍️ <\/span><\/span>Type-I Error \u0915\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e \u0915\u092e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0935\u0948\u091c\u094d\u091e\u093e\u0928\u093f\u0915 \u090f\u0935\u0902 \u0935\u093f\u0936\u094d\u0935\u0938\u0928\u0940\u092f \u092a\u0930\u093f\u0923\u093e\u092e \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0938\u093e\u092e\u093e\u091c\u093f\u0915 \u090f\u0935\u0902 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0935\u093f\u091c\u094d\u091e\u093e\u0928\u094b\u0902 \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u092a\u0915 \u0909\u092a\u092f\u094b\u0917\u0964<\/span><\/p>\n

ANOVA \u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0901 (Limitations)<\/span><\/strong><\/span><\/p>\n

✍️ <\/span><\/span>\u0915\u0947\u0935\u0932 \u092f\u0939 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0905\u0902\u0924\u0930 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902; \u0915\u094c\u0928-\u0938\u0947 \u0938\u092e\u0942\u0939 \u0905\u0932\u0917 \u0939\u0948\u0902, \u092f\u0939 \u0928\u0939\u0940\u0902 \u092c\u0924\u093e\u0924\u093e\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u0938\u092e\u093e\u0928 \u0935\u093f\u091a\u0930\u0923 (Homogeneity) \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0964<\/span><\/p>\n

✍️ <\/span><\/span>Outliers \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n

✍️ <\/span><\/span>\u092f\u0926\u093f ANOVA \u0938\u093e\u0930\u094d\u0925\u0915 \u0939\u094b, \u0924\u094b Post Hoc Test (\u091c\u0948\u0938\u0947 Tukey Test) \u0915\u0930\u0928\u093e \u092a\u0921\u093c\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

ANOVA \u090f\u0935\u0902 t-Test \u092e\u0947\u0902 \u0905\u0902\u0924\u0930<\/span><\/strong><\/span><\/p>\n\n\n\n\n\n\n\n
\u0906\u0927\u093e\u0930<\/span><\/strong><\/td>\nANOVA<\/span><\/strong><\/td>\nt-Test<\/span><\/strong><\/td>\n<\/tr>\n
\u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e<\/span><\/strong><\/td>\n3 \u092f\u093e \u0905\u0927\u093f\u0915<\/span><\/strong><\/td>\n2<\/span><\/strong><\/td>\n<\/tr>\n
\u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/span><\/strong><\/td>\nF-Test<\/span><\/strong><\/td>\nt-Test<\/span><\/strong><\/td>\n<\/tr>\n
\u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/span><\/strong><\/td>\n\u0915\u0908 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f \u0915\u0940 \u0924\u0941\u0932\u0928\u093e<\/span><\/strong><\/td>\n\u0926\u094b \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f \u0915\u0940 \u0924\u0941\u0932\u0928\u093e<\/span><\/strong><\/td>\n<\/tr>\n
\u0935\u093f\u0915\u093e\u0938\u0915\u0930\u094d\u0924\u093e<\/span><\/strong><\/td>\nR. A. Fisher<\/span><\/strong><\/td>\nW. S. Gosset (Student)<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

One-Way ANOVA \u0915\u093e \u0909\u0926\u093e\u0939\u0930\u0923 (Solved Example)<\/span><\/h1>\n

\u092a\u094d\u0930\u0936\u094d\u0928 (Example)<\/span><\/strong><\/p>\n

\u00a0 \u00a0\u090f\u0915 \u0936\u094b\u0927\u0915\u0930\u094d\u0924\u093e \u092f\u0939 \u091c\u093e\u0928\u0928\u093e \u091a\u093e\u0939\u0924\u093e \u0939\u0948 \u0915\u093f \u092c\u093f\u0939\u093e\u0930 \u0915\u0947 \u0924\u0940\u0928 \u091c\u093f\u0932\u094b\u0902 (\u092a\u091f\u0928\u093e, \u0917\u092f\u093e \u0914\u0930 \u092e\u0941\u091c\u092b\u094d\u092b\u0930\u092a\u0941\u0930) \u092e\u0947\u0902 \u0917\u0947\u0939\u0942\u0901 \u0915\u0940 \u0914\u0938\u0924 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e (\u0915\u094d\u0935\u093f\u0902\u091f\u0932\/\u0939\u0947\u0915\u094d\u091f\u0947\u092f\u0930) \u092e\u0947\u0902 \u0915\u094b\u0908 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0902\u0924\u0930 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902\u0964<\/span><\/strong><\/p>\n

\u0921\u0947\u091f\u093e (Yield in Quintal\/Hectare)<\/span><\/strong><\/span><\/h3>\n\n\n\n\n\n\n
\u092a\u091f\u0928\u093e<\/span><\/strong><\/td>\n\u0917\u092f\u093e<\/span><\/strong><\/td>\n\u092e\u0941\u091c\u092b\u094d\u092b\u0930\u092a\u0941\u0930<\/span><\/strong><\/td>\n<\/tr>\n
25<\/span><\/strong><\/td>\n20<\/span><\/strong><\/td>\n30<\/span><\/strong><\/td>\n<\/tr>\n
27<\/span><\/strong><\/td>\n22<\/span><\/strong><\/td>\n32<\/span><\/strong><\/td>\n<\/tr>\n
26<\/span><\/strong><\/td>\n21<\/span><\/strong><\/td>\n31<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Step-1 : Hypothesis (\u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e)<\/span><\/strong><\/span><\/p>\n

H\u2080 (Null Hypothesis):<\/span><\/strong><\/p>\n

\u00a0 \u00a0\u0924\u0940\u0928\u094b\u0902 \u091c\u093f\u0932\u094b\u0902 \u0915\u0940 \u0914\u0938\u0924 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/span><\/p>\n

H\u2081 (Alternative Hypothesis):<\/strong><\/span><\/p>\n

\u00a0 \u00a0\u0915\u092e-\u0938\u0947-\u0915\u092e \u090f\u0915 \u091c\u093f\u0932\u0947 \u0915\u0940 \u0914\u0938\u0924 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e \u0905\u0928\u094d\u092f \u0938\u0947 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964<\/span><\/p>\n

Step-2 : \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u092e\u0942\u0939 \u0915\u093e Mean \u0928\u093f\u0915\u093e\u0932\u0947\u0902<\/span><\/p>\n

\u092a\u091f\u0928\u093e<\/strong><\/span><\/p>\n

X\u03041<\/sub> =\u00a0\u00a0
\n25 + 27 + 26<\/span>3
\n<\/span><\/span><\/div>\n
= 26<\/span><\/div>\n

\u0917\u092f\u093e<\/strong><\/span><\/p>\n

X\u03042 =\u00a0\u00a0
\n20 + 22 + 21<\/span>3
\n<\/span><\/span><\/div>\n
= 21<\/span><\/div>\n

\u092e\u0941\u091c\u092b\u094d\u092b\u0930\u092a\u0941\u0930<\/strong><\/span><\/p>\n

X\u03043 =\u00a0\u00a0
\n30 + 32 + 31<\/span>3
\n<\/span><\/span><\/div>\n
= 31<\/span><\/div>\n

Grand Mean (\u0938\u0902\u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0927\u094d\u092f)<\/span><\/strong><\/span><\/p>\n

\u00a0 \u0938\u092d\u0940 9 \u092e\u093e\u0928\u094b\u0902 \u0915\u093e \u092f\u094b\u0917<\/strong><\/span><\/p>\n

\u00a0= 25+27+26+20+22+21+30+32+31<\/strong><\/span><\/p>\n

\u00a0= 234<\/strong><\/span><\/p>\n

X\u0304 =\u00a0
\n234<\/span>9
\n<\/span><\/strong><\/span>
\n= 26<\/strong><\/span><\/div>\n

Step-3 : Between Group Sum of Squares (SSB)<\/strong><\/span><\/p>\n

\u0938\u0942\u0924\u094d\u0930<\/span><\/p>\n

SSB = \u2211 n(X\u0304i<\/sub>-X\u0304)2<\/sup><\/strong><\/span><\/p>\n

\u091c\u0939\u093e\u0901<\/span><\/p>\n

n = 3<\/span><\/p>\n

\u092a\u091f\u0928\u093e<\/span><\/strong><\/p>\n

3(26 \u2212 26)2<\/sup> = 0<\/span><\/strong><\/div>\n

\u0917\u092f\u093e<\/span><\/strong><\/p>\n

3(21 \u2212 26)2<\/sup><\/div>\n

= 3\u00d725<\/span><\/strong><\/p>\n

= 75<\/span><\/strong><\/p>\n

\u092e\u0941\u091c\u092b\u094d\u092b\u0930\u092a\u0941\u0930<\/strong><\/span><\/p>\n

3(31 \u2212 26)2<\/sup><\/span><\/strong><\/p>\n

= 3\u00d725<\/span><\/strong><\/p>\n

= 75<\/span><\/strong><\/p>\n

\u0905\u0924\u0903<\/span><\/p>\n

SSB = 0+75+75 = 150<\/strong><\/span><\/p>\n

Step-4 : Within Group Sum of Squares (SSW)<\/strong><\/span><\/p>\n

\u092a\u091f\u0928\u093e<\/strong><\/p>\n

 <\/p>\n

(25 \u2212 26)2<\/sup> + (27 \u2212 26)2<\/sup> + (26 \u2212 26)2<\/sup><\/span><\/strong><\/div>\n

=1+1+0 = 2<\/span><\/p>\n

\u0917\u092f\u093e<\/strong><\/span><\/p>\n

(20 \u2212 21)2<\/sup> + (22 \u2212 21)2<\/sup> + (21 \u2212 21)2<\/sup><\/span><\/strong><\/p>\n

= 1+1+0 = 2<\/span><\/strong><\/p>\n

\u092e\u0941\u091c\u092b\u094d\u092b\u0930\u092a\u0941\u0930<\/span><\/strong><\/p>\n

(30 \u2212 31)2<\/sup> + (32 \u2212 31)2<\/sup> + (31 \u2212 31)2<\/sup><\/span><\/strong><\/p>\n

= 1+1+0 <\/span><\/strong>= 2<\/span><\/strong><\/p>\n

\u0905\u0924\u0903 <\/span><\/p>\n

SSW = 2+2+2 = 6<\/strong><\/span><\/p>\n

Step-5 : Total Sum of Squares<\/span><\/strong><\/p>\n

SST = SSB+SSW<\/span><\/span><\/span><\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0= 150+6<\/span><\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0= 156<\/span><\/strong><\/p>\n

Step-6 : Degree of Freedom (df)<\/strong><\/span><\/p>\n

Number of Groups (k) = 3<\/span><\/strong><\/p>\n

Total Observation (N) = 9<\/span><\/strong><\/p>\n

Between Groups<\/h3>\n

df = k\u22121<\/span><\/span><\/span><\/strong><\/p>\n

\u00a0 \u00a0 \u00a0= 3\u22121<\/span><\/strong><\/p>\n

\u00a0 \u00a0 \u00a0= 2<\/span><\/strong><\/p>\n

Within Groups<\/h3>\n

df = N\u2212k<\/span><\/span><\/span><\/strong><\/p>\n

\u00a0 \u00a0 = 9\u22123<\/span><\/strong><\/p>\n

\u00a0 \u00a0 = 6<\/span><\/strong><\/p>\n

Step-7 : Mean Square \u0928\u093f\u0915\u093e\u0932\u0947\u0902<\/strong><\/span><\/h2>\n

Mean Square Between<\/h3>\n

MSB = 150\/2 = 75<\/span><\/span><\/span><\/strong><\/p>\n

Mean Square Within<\/h3>\n

MSW = 6\/6 = 1<\/span><\/span><\/span><\/strong><\/p>\n

Step-8 : F-value \u0928\u093f\u0915\u093e\u0932\u0947\u0902<\/strong><\/span><\/h2>\n

F = MSB\/MSW<\/span><\/span><\/span><\/strong><\/p>\n

F = <\/span><\/span><\/span>75\/1<\/span><\/span><\/span><\/span><\/strong><\/p>\n

\u00a0 = 75<\/span><\/span><\/span><\/strong><\/p>\n

Step-9 : ANOVA Table<\/strong><\/span><\/p>\n\n\n\n\n\n\n
Source<\/span><\/td>\nSS<\/span><\/td>\ndf<\/span><\/td>\nMS<\/span><\/td>\nF<\/span><\/td>\n<\/tr>\n
Between Groups<\/span><\/td>\n150<\/span><\/td>\n2<\/span><\/td>\n75<\/span><\/td>\n75<\/strong><\/span><\/td>\n<\/tr>\n
Within Groups<\/span><\/td>\n6<\/span><\/td>\n6<\/span><\/td>\n1<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
Total<\/span><\/td>\n156<\/span><\/td>\n8<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Step-10 : Decision (\u0928\u093f\u0930\u094d\u0923\u092f)<\/span><\/p>\n

5% \u092e\u0939\u0924\u094d\u0935 \u0938\u094d\u0924\u0930 (\u03b1 = 0.05) \u092a\u0930<\/span><\/p>\n

df\u2081 = 2<\/span><\/p>\n

df\u2082 = 6<\/span><\/p>\n

F-Table \u2248 5.14<\/span><\/p>\n

Fcal = 75<\/span><\/p>\n

\u0915\u094d\u092f\u094b\u0902\u0915\u093f 75 > 5.14<\/span><\/p>\n

\u00a0\u0905\u0924\u0903 Null Hypothesis (H\u2080) \u0905\u0938\u094d\u0935\u0940\u0915\u093e\u0930 (Reject) \u0915\u0940 \u091c\u093e\u090f\u0917\u0940<\/span><\/p>\n

Conclusion (\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937):<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u092a\u091f\u0928\u093e, \u0917\u092f\u093e \u090f\u0935\u0902 \u092e\u0941\u091c\u092b\u094d\u092b\u0930\u092a\u0941\u0930 \u091c\u093f\u0932\u094b\u0902 \u0915\u0940 \u0917\u0947\u0939\u0942\u0901 \u0915\u0940 \u0914\u0938\u0924 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e \u092e\u0947\u0902 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f<\/a> \u0930\u0942\u092a \u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0902\u0924\u0930<\/a> (Statistically Significant Difference) \u092a\u093e\u092f\u093e \u0917\u092f\u093e\u0964 \u0905\u0930\u094d\u0925\u093e\u0924 \u0924\u0940\u0928\u094b\u0902 \u091c\u093f\u0932\u094b\u0902 \u0915\u0940 \u0909\u0924\u094d\u092a\u093e\u0926\u0915\u0924\u093e \u0938\u092e\u093e\u0928 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/span><\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Analysis of Variance (ANOVA) – \u0935\u093f\u091a\u0930\u0923 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923   \u092a\u0930\u093f\u091a\u092f (Introduction) \u00a0 \u00a0 \u00a0 Analysis of Variance (ANOVA) \u092f\u093e \u0935\u093f\u091a\u0930\u0923 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093e\u092e\u093f\u0924\u0940\u092f (Parametric) \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0939\u0948, \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0924\u0940\u0928 \u092f\u093e \u0924\u0940\u0928 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0938\u092e\u0942\u0939\u094b\u0902 (Groups) \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u094b\u0902 (Means) \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u00a0 \u00a0 \u00a0ANOVA \u0915\u093e \u0935\u093f\u0915\u093e\u0938 \u092a\u094d\u0930\u0938\u093f\u0926\u094d\u0927 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u0935\u093f\u0926\u094d Sir […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[53,74,162],"tags":[],"class_list":["post-21649","post","type-post","status-publish","format-standard","hentry","category-ba-semester-paper-vii","category-pg-semester-3","category-research-methodology"],"acf":{"test_duration":60,"q1_question":"","q1_option_a":"","q1_option_b":"","q1_option_c":"","q1_option_d":"","q1_correct":"","q1_explanation":"","q2_question":"","q2_option_a":"","q2_option_b":"","q2_option_c":"","q2_option_d":"","q2_correct":"","q2_explanation":"","q3_question":"","q3_option_a":"","q3_option_b":"","q3_option_c":"","q3_option_d":"","q3_correct":"","q3_explanation":"","q4_question":"","q4_option_a":"","q4_option_b":"","q4_option_c":"","q4_option_d":"","q4_correct":"","q4_explanation":"","q5_question":"","q5_option_a":"","q5_option_b":"","q5_option_c":"","q5_option_d":"","q5_correct":"","q5_explanation":"","q6_question":"","q6_option_a":"","q6_option_b":"","q6_option_c":"","q6_option_d":"","q6_correct":"","q6_explanation":"","q7_question":"","q7_option_a":"","q7_option_b":"","q7_option_c":"","q7_option_d":"","q7_correct":"","q7_explanation":"","q8_question":"","q8_option_a":"","q8_option_b":"","q8_option_c":"","q8_option_d":"","q8_correct":"","q8_explanation":"","q9_question":"","q9_option_a":"","q9_option_b":"","q9_option_c":"","q9_option_d":"","q9_correct":"","q9_explanation":"","q10_question":"","q10_option_a":"","q10_option_b":"","q10_option_c":"","q10_option_d":"","q10_correct":"","q10_explanation":"","q11_question":"","q11_option_a":"","q11_option_b":"","q11_option_c":"","q11_option_d":"","q11_correct":"","q11_explanation":"","q12_question":"","q12_option_a":"","q12_option_b":"","q12_option_c":"","q12_option_d":"","q12_correct":"","q12_explanation":"","q13_question":"","q13_option_a":"","q13_option_b":"","q13_option_c":"","q13_option_d":"","q13_correct":"","q13_explanation":"","q14_question":"","q14_option_a":"","q14_option_b":"","q14_option_c":"","q14_option_d":"","q14_correct":"","q14_explanation":"","q15_question":"","q15_option_a":"","q15_option_b":"","q15_option_c":"","q15_option_d":"","q15_correct":"","q15_explanation":"","q16_question":"","q16_option_a":"","q16_option_b":"","q16_option_c":"","q16_option_d":"","q16_correct":"","q16_explanation":"","q17_question":"","q17_option_a":"","q17_option_b":"","q17_option_c":"","q17_option_d":"","q17_correct":"","q17_explanation":"","q18_question":"","q18_option_a":"","q18_option_b":"","q18_option_c":"","q18_option_d":"","q18_correct":"","q18_explanation":"","q19_question":"","q19_option_a":"","q19_option_b":"","q19_option_c":"","q19_option_d":"","q19_correct":"","q19_explanation":"","q20_question":"","q20_option_a":"","q20_option_b":"","q20_option_c":"","q20_option_d":"","q20_correct":"","q20_explanation":"","q21_question":"","q21_option_a":"","q21_option_b":"","q21_option_c":"","q21_option_d":"","q21_correct":"","q21_explanation":"","q22_question":"","q22_option_a":"","q22_option_b":"","q22_option_c":"","q22_option_d":"","q22_correct":"","q22_explanation":"","q23_question":"","q23_option_a":"","q23_option_b":"","q23_option_c":"","q23_option_d":"","q23_correct":"","q23_explanation":"","q24_question":"","q24_option_a":"","q24_option_b":"","q24_option_c":"","q24_option_d":"","q24_correct":"","q24_explanation":"","q25_question":"","q25_option_a":"","q25_option_b":"","q25_option_c":"","q25_option_d":"","q25_correct":"","q25_explanation":"","q26_question":"","q26_option_a":"","q26_option_b":"","q26_option_c":"","q26_option_d":"","q26_correct":"","q26_explanation":"","q27_question":"","q27_option_a":"","q27_option_b":"","q27_option_c":"","q27_option_d":"","q27_correct":"","q27_explanation":"","q28_question":"","q28_option_a":"","q28_option_b":"","q28_option_c":"","q28_option_d":"","q28_correct":"","q28_explanation":"","q29_question":"","q29_option_a":"","q29_option_b":"","q29_option_c":"","q29_option_d":"","q29_correct":"","q29_explanation":"","q30_question":"","q30_option_a":"","q30_option_b":"","q30_option_c":"","q30_option_d":"","q30_correct":"","q30_explanation":"","q31_question":"","q31_option_a":"","q31_option_b":"","q31_option_c":"","q31_option_d":"","q31_correct":"","q31_explanation":"","q32_question":"","q32_option_a":"","q32_option_b":"","q32_option_c":"","q32_option_d":"","q32_correct":"","q32_explanation":"","q33_question":"","q33_option_a":"","q33_option_b":"","q33_option_c":"","q33_option_d":"","q33_correct":"","q33_explanation":"","q34_question":"","q34_option_a":"","q34_option_b":"","q34_option_c":"","q34_option_d":"","q34_correct":"","q34_explanation":"","q35_question":"","q35_option_a":"","q35_option_b":"","q35_option_c":"","q35_option_d":"","q35_correct":"","q35_explanation":"","q36_question":"","q36_option_a":"","q36_option_b":"","q36_option_c":"","q36_option_d":"","q36_correct":"","q36_explanation":"","q37_question":"","q37_option_a":"","q37_option_b":"","q37_option_c":"","q37_option_d":"","q37_correct":"","q37_explanation":"","q38_question":"","q38_option_a":"","q38_option_b":"","q38_option_c":"","q38_option_d":"","q38_correct":"","q38_explanation":"","q39_question":"","q39_option_a":"","q39_option_b":"","q39_option_c":"","q39_option_d":"","q39_correct":"","q39_explanation":"","q40_question":"","q40_option_a":"","q40_option_b":"","q40_option_c":"","q40_option_d":"","q40_correct":"","q40_explanation":"","q41_question":"","q41_option_a":"","q41_option_b":"","q41_option_c":"","q41_option_d":"","q41_correct":"","q41_explanation":"","q42_question":"","q42_option_a":"","q42_option_b":"","q42_option_c":"","q42_option_d":"","q42_correct":"","q42_explanation":"","q43_question":"","q43_option_a":"","q43_option_b":"","q43_option_c":"","q43_option_d":"","q43_correct":"","q43_explanation":"","q44_question":"","q44_option_a":"","q44_option_b":"","q44_option_c":"","q44_option_d":"","q44_correct":"","q44_explanation":"","q45_question":"","q45_option_a":"","q45_option_b":"","q45_option_c":"","q45_option_d":"","q45_correct":"","q45_explanation":"","q46_question":"","q46_option_a":"","q46_option_b":"","q46_option_c":"","q46_option_d":"","q46_correct":"","q46_explanation":"","q47_question":"","q47_option_a":"","q47_option_b":"","q47_option_c":"","q47_option_d":"","q47_correct":"","q47_explanation":"","q48_question":"","q48_option_a":"","q48_option_b":"","q48_option_c":"","q48_option_d":"","q48_correct":"","q48_explanation":"","q49_question":"","q49_option_a":"","q49_option_b":"","q49_option_c":"","q49_option_d":"","q49_correct":"","q49_explanation":"","q50_question":"","q50_option_a":"","q50_option_b":"","q50_option_c":"","q50_option_d":"","q50_correct":"","q50_explanation":"","q51_question":"","q51_option_a":"","q51_option_b":"","q51_option_c":"","q51_option_d":"","q51_correct":"","q51_explanation":"","q52_question":"","q52_option_a":"","q52_option_b":"","q52_option_c":"","q52_option_d":"","q52_correct":"","q52_explanation":"","q53_question":"","q53_option_a":"","q53_option_b":"","q53_option_c":"","q53_option_d":"","q53_correct":"","q53_explanation":"","q54_question":"","q54_option_a":"","q54_option_b":"","q54_option_c":"","q54_option_d":"","q54_correct":"","q54_explanation":"","q55_question":"","q55_option_a":"","q55_option_b":"","q55_option_c":"","q55_option_d":"","q55_correct":"","q55_explanation":"","q56_question":"","q56_option_a":"","q56_option_b":"","q56_option_c":"","q56_option_d":"","q56_correct":"","q56_explanation":"","q57_question":"","q57_option_a":"","q57_option_b":"","q57_option_c":"","q57_option_d":"","q57_correct":"","q57_explanation":"","q58_question":"","q58_option_a":"","q58_option_b":"","q58_option_c":"","q58_option_d":"","q58_correct":"","q58_explanation":"","q59_question":"","q59_option_a":"","q59_option_b":"","q59_option_c":"","q59_option_d":"","q59_correct":"","q59_explanation":"","q60_question":"","q60_option_a":"","q60_option_b":"","q60_option_c":"","q60_option_d":"","q60_correct":"","q60_explanation":"","q61_question":"","q61_option_a":"","q61_option_b":"","q61_option_c":"","q61_option_d":"","q61_correct":"","q61_explanation":"","q62_question":"","q62_option_a":"","q62_option_b":"","q62_option_c":"","q62_option_d":"","q62_correct":"","q62_explanation":"","q63_question":"","q63_option_a":"","q63_option_b":"","q63_option_c":"","q63_option_d":"","q63_correct":"","q63_explanation":"","q64_question":"","q64_option_a":"","q64_option_b":"","q64_option_c":"","q64_option_d":"","q64_correct":"","q64_explanation":"","q65_question":"","q65_option_a":"","q65_option_b":"","q65_option_c":"","q65_option_d":"","q65_correct":"","q65_explanation":"","q66_question":"","q66_option_a":"","q66_option_b":"","q66_option_c":"","q66_option_d":"","q66_correct":"","q66_explanation":"","q67_question":"","q67_option_a":"","q67_option_b":"","q67_option_c":"","q67_option_d":"","q67_correct":"","q67_explanation":"","q68_question":"","q68_option_a":"","q68_option_b":"","q68_option_c":"","q68_option_d":"","q68_correct":"","q68_explanation":"","q69_question":"","q69_option_a":"","q69_option_b":"","q69_option_c":"","q69_option_d":"","q69_correct":"","q69_explanation":"","q70_question":"","q70_option_a":"","q70_option_b":"","q70_option_c":"","q70_option_d":"","q70_correct":"","q70_explanation":"","q71_question":"","q71_option_a":"","q71_option_b":"","q71_option_c":"","q71_option_d":"","q71_correct":"","q71_explanation":"","q72_question":"","q72_option_a":"","q72_option_b":"","q72_option_c":"","q72_option_d":"","q72_correct":"","q72_explanation":"","q73_question":"","q73_option_a":"","q73_option_b":"","q73_option_c":"","q73_option_d":"","q73_correct":"","q73_explanation":"","q74_question":"","q74_option_a":"","q74_option_b":"","q74_option_c":"","q74_option_d":"","q74_correct":"","q74_explanation":"","q75_question":"","q75_option_a":"","q75_option_b":"","q75_option_c":"","q75_option_d":"","q75_correct":"","q75_explanation":"","q76_question":"","q76_option_a":"","q76_option_b":"","q76_option_c":"","q76_option_d":"","q76_correct":"","q76_explanation":"","q77_question":"","q77_option_a":"","q77_option_b":"","q77_option_c":"","q77_option_d":"","q77_correct":"","q77_explanation":"","q78_question":"","q78_option_a":"","q78_option_b":"","q78_option_c":"","q78_option_d":"","q78_correct":"","q78_explanation":"","q79_question":"","q79_option_a":"","q79_option_b":"","q79_option_c":"","q79_option_d":"","q79_correct":"","q79_explanation":"","q80_question":"","q80_option_a":"","q80_option_b":"","q80_option_c":"","q80_option_d":"","q80_correct":"","q80_explanation":"","q81_question":"","q81_option_a":"","q81_option_b":"","q81_option_c":"","q81_option_d":"","q81_correct":"","q81_explanation":"","q82_question":"","q82_option_a":"","q82_option_b":"","q82_option_c":"","q82_option_d":"","q82_correct":"","q82_explanation":"","q83_question":"","q83_option_a":"","q83_option_b":"","q83_option_c":"","q83_option_d":"","q83_correct":"","q83_explanation":"","q84_question":"","q84_option_a":"","q84_option_b":"","q84_option_c":"","q84_option_d":"","q84_correct":"","q84_explanation":"","q85_question":"","q85_option_a":"","q85_option_b":"","q85_option_c":"","q85_option_d":"","q85_correct":"","q85_explanation":"","q86_question":"","q86_option_a":"","q86_option_b":"","q86_option_c":"","q86_option_d":"","q86_correct":"","q86_explanation":"","q87_question":"","q87_option_a":"","q87_option_b":"","q87_option_c":"","q87_option_d":"","q87_correct":"","q87_explanation":"","q88_question":"","q88_option_a":"","q88_option_b":"","q88_option_c":"","q88_option_d":"","q88_correct":"","q88_explanation":"","q89_question":"","q89_option_a":"","q89_option_b":"","q89_option_c":"","q89_option_d":"","q89_correct":"","q89_explanation":"","q90_question":"","q90_option_a":"","q90_option_b":"","q90_option_c":"","q90_option_d":"","q90_correct":"","q90_explanation":"","q91_question":"","q91_option_a":"","q91_option_b":"","q91_option_c":"","q91_option_d":"","q91_correct":"","q91_explanation":"","q92_question":"","q92_option_a":"","q92_option_b":"","q92_option_c":"","q92_option_d":"","q92_correct":"","q92_explanation":"","q93_question":"","q93_option_a":"","q93_option_b":"","q93_option_c":"","q93_option_d":"","q93_correct":"","q93_explanation":"","q94_question":"","q94_option_a":"","q94_option_b":"","q94_option_c":"","q94_option_d":"","q94_correct":"","q94_explanation":"","q95_question":"","q95_option_a":"","q95_option_b":"","q95_option_c":"","q95_option_d":"","q95_correct":"","q95_explanation":"","q96_question":"","q96_option_a":"","q96_option_b":"","q96_option_c":"","q96_option_d":"","q96_correct":"","q96_explanation":"","q97_question":"","q97_option_a":"","q97_option_b":"","q97_option_c":"","q97_option_d":"","q97_correct":"","q97_explanation":"","q98_question":"","q98_option_a":"","q98_option_b":"","q98_option_c":"","q98_option_d":"","q98_correct":"","q98_explanation":"","q99_question":"","q99_option_a":"","q99_option_b":"","q99_option_c":"","q99_option_d":"","q99_correct":"","q99_explanation":"","q100_question":"","q100_option_a":"","q100_option_b":"","q100_option_c":"","q100_option_d":"","q100_correct":"","q100_explanation":""},"_links":{"self":[{"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/posts\/21649","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/comments?post=21649"}],"version-history":[{"count":24,"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/posts\/21649\/revisions"}],"predecessor-version":[{"id":22284,"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/posts\/21649\/revisions\/22284"}],"wp:attachment":[{"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/media?parent=21649"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/categories?post=21649"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geographynotespdf.com\/cms\/wp-json\/wp\/v2\/tags?post=21649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}