1 Sampling & Survey Techniques

1.1 Field Sampling Error Simulation

Imagine you are part of a field research team assigned to survey the usage level of online transportation applications in 3 medium-sized cities in Sumatra. The total sample target is 600 respondents, with 200 respondents from each city. However, after 2 weeks of conducting the survey, you find the following:

In City A, the team successfully obtained 250 respondents.

In City B, only 120 respondents were interviewed.

In City C, 180 respondents.

ID Responden Kota Gender Umur Penggunaan Harian Bobot
K001 Kota A P 47 5 0.733
K002 Kota A L 58 3 0.733
K003 Kota A L 55 0 0.733
K004 Kota A P 41 1 0.733
K005 Kota A P 57 2 0.733
K006 Kota A P 20 0 0.733
K007 Kota A P 32 4 0.733
K008 Kota A L 23 6 0.733
K009 Kota A P 48 6 0.733
K010 Kota A P 46 2 0.733
K011 Kota A P 30 4 0.733
K012 Kota A P 57 6 0.733
K013 Kota A P 49 2 0.733
K014 Kota A L 22 3 0.733
K015 Kota A P 28 3 0.733
K016 Kota A P 38 4 0.733
K017 Kota A P 51 4 0.733
K018 Kota A L 23 5 0.733
K019 Kota A P 52 2 0.733
K020 Kota A P 37 2 0.733
K021 Kota A P 36 1 0.733
K022 Kota A L 45 5 0.733
K023 Kota A P 32 4 0.733
K024 Kota A L 42 4 0.733
K025 Kota A L 54 0 0.733
K026 Kota A L 54 1 0.733
K027 Kota A L 38 6 0.733
K028 Kota A P 21 5 0.733
K029 Kota A L 45 0 0.733
K030 Kota A P 24 0 0.733
K031 Kota A P 29 4 0.733
K032 Kota A P 33 3 0.733
K033 Kota A P 30 0 0.733
K034 Kota A P 48 0 0.733
K035 Kota A P 27 0 0.733
K036 Kota A P 57 0 0.733
K037 Kota A P 37 6 0.733
K038 Kota A P 51 2 0.733
K039 Kota A L 41 3 0.733
K040 Kota A P 55 2 0.733
K041 Kota A L 28 2 0.733
K042 Kota A L 38 0 0.733
K043 Kota A P 29 5 0.733
K044 Kota A P 23 0 0.733
K045 Kota A L 47 1 0.733
K046 Kota A P 59 0 0.733
K047 Kota A P 51 1 0.733
K048 Kota A L 38 0 0.733
K049 Kota A P 41 4 0.733
K050 Kota A L 47 5 0.733
K051 Kota A L 38 3 0.733
K052 Kota A L 51 3 0.733
K053 Kota A L 41 2 0.733
K054 Kota A L 60 0 0.733
K055 Kota A P 25 1 0.733
K056 Kota A L 45 3 0.733
K057 Kota A P 31 4 0.733
K058 Kota A L 45 1 0.733
K059 Kota A P 43 6 0.733
K060 Kota A P 19 1 0.733
K061 Kota A L 20 5 0.733
K062 Kota A L 33 5 0.733
K063 Kota A L 38 5 0.733
K064 Kota A P 35 0 0.733
K065 Kota A P 43 2 0.733
K066 Kota A L 26 6 0.733
K067 Kota A P 20 2 0.733
K068 Kota A L 21 5 0.733
K069 Kota A L 40 1 0.733
K070 Kota A P 52 6 0.733
K071 Kota A L 51 0 0.733
K072 Kota A P 46 5 0.733
K073 Kota A L 31 5 0.733
K074 Kota A L 19 6 0.733
K075 Kota A P 29 3 0.733
K076 Kota A L 32 0 0.733
K077 Kota A L 34 1 0.733
K078 Kota A P 53 2 0.733
K079 Kota A L 49 6 0.733
K080 Kota A P 24 3 0.733
K081 Kota A P 23 6 0.733
K082 Kota A P 20 2 0.733
K083 Kota A P 49 6 0.733
K084 Kota A P 48 2 0.733
K085 Kota A P 48 4 0.733
K086 Kota A L 23 4 0.733
K087 Kota A L 59 4 0.733
K088 Kota A P 24 6 0.733
K089 Kota A L 43 3 0.733
K090 Kota A L 60 1 0.733
K091 Kota A L 43 1 0.733
K092 Kota A P 58 2 0.733
K093 Kota A P 41 4 0.733
K094 Kota A L 57 2 0.733
K095 Kota A L 38 1 0.733
K096 Kota A L 36 0 0.733
K097 Kota A L 51 4 0.733
K098 Kota A P 21 3 0.733
K099 Kota A L 50 0 0.733
K100 Kota A L 36 6 0.733
K101 Kota A L 59 1 0.733
K102 Kota A P 27 0 0.733
K103 Kota A P 27 2 0.733
K104 Kota A P 41 6 0.733
K105 Kota A L 26 0 0.733
K106 Kota A L 38 2 0.733
K107 Kota A P 35 4 0.733
K108 Kota A P 59 5 0.733
K109 Kota A P 57 0 0.733
K110 Kota A P 48 6 0.733
K111 Kota A L 58 2 0.733
K112 Kota A L 42 3 0.733
K113 Kota A L 48 4 0.733
K114 Kota A P 21 6 0.733
K115 Kota A L 24 6 0.733
K116 Kota A P 29 6 0.733
K117 Kota A L 37 3 0.733
K118 Kota A P 22 6 0.733
K119 Kota A L 35 6 0.733
K120 Kota A L 18 2 0.733
K121 Kota A P 50 0 0.733
K122 Kota A L 42 5 0.733
K123 Kota A L 29 3 0.733
K124 Kota A L 52 6 0.733
K125 Kota A L 19 3 0.733
K126 Kota A P 18 4 0.733
K127 Kota A P 37 1 0.733
K128 Kota A P 33 4 0.733
K129 Kota A L 38 5 0.733
K130 Kota A P 43 0 0.733
K131 Kota A L 40 0 0.733
K132 Kota A L 19 6 0.733
K133 Kota A L 53 5 0.733
K134 Kota A L 54 5 0.733
K135 Kota A L 60 0 0.733
K136 Kota A P 23 0 0.733
K137 Kota A P 49 4 0.733
K138 Kota A P 19 6 0.733
K139 Kota A L 46 1 0.733
K140 Kota A L 56 5 0.733
K141 Kota A P 35 2 0.733
K142 Kota A P 24 3 0.733
K143 Kota A P 32 3 0.733
K144 Kota A P 48 5 0.733
K145 Kota A P 30 3 0.733
K146 Kota A L 28 5 0.733
K147 Kota A P 40 3 0.733
K148 Kota A P 31 2 0.733
K149 Kota A L 18 2 0.733
K150 Kota A P 57 3 0.733
K151 Kota A L 23 0 0.733
K152 Kota A L 58 2 0.733
K153 Kota A P 23 4 0.733
K154 Kota A P 34 0 0.733
K155 Kota A L 55 0 0.733
K156 Kota A P 57 4 0.733
K157 Kota A L 58 2 0.733
K158 Kota A P 57 2 0.733
K159 Kota A L 50 3 0.733
K160 Kota A L 27 2 0.733
K161 Kota A L 37 3 0.733
K162 Kota A P 36 4 0.733
K163 Kota A L 48 2 0.733
K164 Kota A L 30 3 0.733
K165 Kota A P 27 5 0.733
K166 Kota A L 57 1 0.733
K167 Kota A P 52 6 0.733
K168 Kota A L 55 2 0.733
K169 Kota A P 26 2 0.733
K170 Kota A L 50 5 0.733
K171 Kota A L 25 3 0.733
K172 Kota A L 26 6 0.733
K173 Kota A L 39 1 0.733
K174 Kota A P 56 4 0.733
K175 Kota A P 39 5 0.733
K176 Kota A L 27 4 0.733
K177 Kota A P 43 4 0.733
K178 Kota A P 21 5 0.733
K179 Kota A L 24 6 0.733
K180 Kota A P 33 6 0.733
K181 Kota A L 19 6 0.733
K182 Kota A P 44 6 0.733
K183 Kota A P 34 1 0.733
K184 Kota A L 28 5 0.733
K185 Kota A L 56 3 0.733
K186 Kota A P 20 1 0.733
K187 Kota A L 40 6 0.733
K188 Kota A L 30 3 0.733
K189 Kota A L 43 6 0.733
K190 Kota A L 52 0 0.733
K191 Kota A L 27 3 0.733
K192 Kota A P 24 4 0.733
K193 Kota A P 55 2 0.733
K194 Kota A P 53 4 0.733
K195 Kota A L 58 2 0.733
K196 Kota A L 54 3 0.733
K197 Kota A P 27 5 0.733
K198 Kota A L 24 0 0.733
K199 Kota A L 32 4 0.733
K200 Kota A P 40 6 0.733
K201 Kota A P 44 0 0.733
K202 Kota A P 26 4 0.733
K203 Kota A P 50 6 0.733
K204 Kota A L 29 0 0.733
K205 Kota A L 56 0 0.733
K206 Kota A L 59 5 0.733
K207 Kota A L 39 1 0.733
K208 Kota A P 26 3 0.733
K209 Kota A P 48 4 0.733
K210 Kota A P 22 0 0.733
K211 Kota A P 47 2 0.733
K212 Kota A P 38 0 0.733
K213 Kota A L 42 3 0.733
K214 Kota A L 30 3 0.733
K215 Kota A P 29 4 0.733
K216 Kota A P 28 4 0.733
K217 Kota A L 37 1 0.733
K218 Kota A L 42 5 0.733
K219 Kota A L 57 6 0.733
K220 Kota A P 34 4 0.733
K221 Kota A L 50 5 0.733
K222 Kota A L 21 6 0.733
K223 Kota A L 50 6 0.733
K224 Kota A L 48 5 0.733
K225 Kota A P 35 2 0.733
K226 Kota A P 42 6 0.733
K227 Kota A P 18 4 0.733
K228 Kota A P 52 1 0.733
K229 Kota A L 51 1 0.733
K230 Kota A P 44 1 0.733
K231 Kota A L 52 5 0.733
K232 Kota A P 53 2 0.733
K233 Kota A L 49 0 0.733
K234 Kota A P 44 0 0.733
K235 Kota A P 23 1 0.733
K236 Kota A P 47 1 0.733
K237 Kota A L 28 5 0.733
K238 Kota A L 23 0 0.733
K239 Kota A L 48 1 0.733
K240 Kota A P 44 3 0.733
K241 Kota A P 32 6 0.733
K242 Kota A L 39 5 0.733
K243 Kota A L 46 1 0.733
K244 Kota A L 27 6 0.733
K245 Kota A P 41 3 0.733
K246 Kota A P 19 1 0.733
K247 Kota A P 55 4 0.733
K248 Kota A P 44 1 0.733
K249 Kota A L 22 4 0.733
K250 Kota A L 47 5 0.733
K001 Kota B L 40 2 1.528
K002 Kota B P 25 6 1.528
K003 Kota B L 42 6 1.528
K004 Kota B L 52 1 1.528
K005 Kota B L 35 3 1.528
K006 Kota B L 47 4 1.528
K007 Kota B L 60 3 1.528
K008 Kota B P 50 4 1.528
K009 Kota B P 45 2 1.528
K010 Kota B L 18 4 1.528
K011 Kota B P 47 6 1.528
K012 Kota B P 38 1 1.528
K013 Kota B L 52 3 1.528
K014 Kota B P 35 2 1.528
K015 Kota B L 60 3 1.528
K016 Kota B L 47 3 1.528
K017 Kota B P 60 5 1.528
K018 Kota B L 49 4 1.528
K019 Kota B P 27 3 1.528
K020 Kota B P 37 0 1.528
K021 Kota B L 45 5 1.528
K022 Kota B L 53 1 1.528
K023 Kota B L 23 2 1.528
K024 Kota B P 60 2 1.528
K025 Kota B P 40 4 1.528
K026 Kota B P 56 6 1.528
K027 Kota B P 22 6 1.528
K028 Kota B P 42 0 1.528
K029 Kota B P 36 0 1.528
K030 Kota B P 42 6 1.528
K031 Kota B P 52 5 1.528
K032 Kota B P 31 1 1.528
K033 Kota B P 56 4 1.528
K034 Kota B P 39 0 1.528
K035 Kota B L 33 4 1.528
K036 Kota B L 28 5 1.528
K037 Kota B L 33 5 1.528
K038 Kota B L 21 1 1.528
K039 Kota B P 24 5 1.528
K040 Kota B P 26 5 1.528
K041 Kota B P 24 1 1.528
K042 Kota B P 34 5 1.528
K043 Kota B L 32 0 1.528
K044 Kota B L 43 3 1.528
K045 Kota B L 28 3 1.528
K046 Kota B P 42 4 1.528
K047 Kota B L 41 6 1.528
K048 Kota B L 34 5 1.528
K049 Kota B L 56 0 1.528
K050 Kota B P 40 0 1.528
K051 Kota B P 46 0 1.528
K052 Kota B P 55 6 1.528
K053 Kota B P 57 2 1.528
K054 Kota B P 26 5 1.528
K055 Kota B L 48 3 1.528
K056 Kota B P 37 3 1.528
K057 Kota B L 49 0 1.528
K058 Kota B L 44 3 1.528
K059 Kota B L 36 2 1.528
K060 Kota B L 34 1 1.528
K061 Kota B L 42 3 1.528
K062 Kota B L 41 5 1.528
K063 Kota B L 40 4 1.528
K064 Kota B L 51 0 1.528
K065 Kota B P 25 2 1.528
K066 Kota B P 41 5 1.528
K067 Kota B P 46 0 1.528
K068 Kota B L 52 1 1.528
K069 Kota B P 31 4 1.528
K070 Kota B L 41 4 1.528
K071 Kota B P 42 3 1.528
K072 Kota B P 27 2 1.528
K073 Kota B P 34 0 1.528
K074 Kota B P 52 5 1.528
K075 Kota B L 18 6 1.528
K076 Kota B P 18 6 1.528
K077 Kota B P 60 6 1.528
K078 Kota B P 20 5 1.528
K079 Kota B L 29 2 1.528
K080 Kota B L 18 4 1.528
K081 Kota B P 40 2 1.528
K082 Kota B L 41 4 1.528
K083 Kota B L 38 1 1.528
K084 Kota B P 41 0 1.528
K085 Kota B P 42 4 1.528
K086 Kota B P 26 4 1.528
K087 Kota B P 42 1 1.528
K088 Kota B L 60 2 1.528
K089 Kota B L 26 2 1.528
K090 Kota B L 50 0 1.528
K091 Kota B P 25 0 1.528
K092 Kota B P 37 4 1.528
K093 Kota B L 53 4 1.528
K094 Kota B P 49 6 1.528
K095 Kota B L 29 2 1.528
K096 Kota B L 31 0 1.528
K097 Kota B L 56 6 1.528
K098 Kota B L 42 6 1.528
K099 Kota B L 59 1 1.528
K100 Kota B P 56 0 1.528
K101 Kota B L 40 5 1.528
K102 Kota B P 56 5 1.528
K103 Kota B L 52 4 1.528
K104 Kota B P 58 2 1.528
K105 Kota B P 40 2 1.528
K106 Kota B P 33 2 1.528
K107 Kota B P 34 4 1.528
K108 Kota B L 29 1 1.528
K109 Kota B P 27 3 1.528
K110 Kota B P 24 3 1.528
K111 Kota B L 33 6 1.528
K112 Kota B P 60 0 1.528
K113 Kota B P 48 1 1.528
K114 Kota B P 39 2 1.528
K115 Kota B P 54 4 1.528
K116 Kota B L 46 0 1.528
K117 Kota B P 58 0 1.528
K118 Kota B P 53 3 1.528
K119 Kota B P 43 3 1.528
K120 Kota B P 54 1 1.528
K001 Kota C P 26 4 1.018
K002 Kota C L 35 6 1.018
K003 Kota C P 38 3 1.018
K004 Kota C L 21 3 1.018
K005 Kota C L 37 6 1.018
K006 Kota C L 37 6 1.018
K007 Kota C P 24 1 1.018
K008 Kota C L 49 5 1.018
K009 Kota C L 49 6 1.018
K010 Kota C P 59 2 1.018
K011 Kota C L 44 5 1.018
K012 Kota C L 45 5 1.018
K013 Kota C P 44 1 1.018
K014 Kota C L 57 5 1.018
K015 Kota C L 33 2 1.018
K016 Kota C L 21 4 1.018
K017 Kota C P 32 3 1.018
K018 Kota C P 43 0 1.018
K019 Kota C P 30 6 1.018
K020 Kota C P 19 2 1.018
K021 Kota C P 48 1 1.018
K022 Kota C P 50 4 1.018
K023 Kota C L 60 5 1.018
K024 Kota C L 56 4 1.018
K025 Kota C L 49 1 1.018
K026 Kota C P 47 0 1.018
K027 Kota C P 46 5 1.018
K028 Kota C L 46 4 1.018
K029 Kota C P 54 0 1.018
K030 Kota C P 60 0 1.018
K031 Kota C P 35 0 1.018
K032 Kota C L 48 1 1.018
K033 Kota C L 22 0 1.018
K034 Kota C L 27 1 1.018
K035 Kota C P 56 1 1.018
K036 Kota C P 38 2 1.018
K037 Kota C P 44 3 1.018
K038 Kota C L 42 4 1.018
K039 Kota C L 22 5 1.018
K040 Kota C P 48 0 1.018
K041 Kota C L 44 4 1.018
K042 Kota C P 59 3 1.018
K043 Kota C P 27 4 1.018
K044 Kota C L 31 3 1.018
K045 Kota C P 41 5 1.018
K046 Kota C P 34 1 1.018
K047 Kota C L 27 2 1.018
K048 Kota C P 44 5 1.018
K049 Kota C P 18 0 1.018
K050 Kota C L 42 5 1.018
K051 Kota C L 39 2 1.018
K052 Kota C P 54 2 1.018
K053 Kota C P 41 4 1.018
K054 Kota C P 27 2 1.018
K055 Kota C L 23 5 1.018
K056 Kota C P 42 6 1.018
K057 Kota C P 53 6 1.018
K058 Kota C L 20 1 1.018
K059 Kota C L 60 5 1.018
K060 Kota C L 35 2 1.018
K061 Kota C L 43 0 1.018
K062 Kota C P 41 1 1.018
K063 Kota C L 32 3 1.018
K064 Kota C L 48 6 1.018
K065 Kota C L 50 6 1.018
K066 Kota C L 36 4 1.018
K067 Kota C L 41 5 1.018
K068 Kota C L 29 1 1.018
K069 Kota C L 37 3 1.018
K070 Kota C P 46 0 1.018
K071 Kota C L 23 4 1.018
K072 Kota C P 41 3 1.018
K073 Kota C P 34 3 1.018
K074 Kota C L 36 0 1.018
K075 Kota C L 40 1 1.018
K076 Kota C L 34 6 1.018
K077 Kota C P 30 5 1.018
K078 Kota C L 36 3 1.018
K079 Kota C P 34 1 1.018
K080 Kota C P 25 0 1.018
K081 Kota C P 30 0 1.018
K082 Kota C L 52 1 1.018
K083 Kota C P 35 4 1.018
K084 Kota C L 56 0 1.018
K085 Kota C L 59 0 1.018
K086 Kota C L 45 5 1.018
K087 Kota C P 58 1 1.018
K088 Kota C L 52 1 1.018
K089 Kota C L 24 2 1.018
K090 Kota C P 57 1 1.018
K091 Kota C P 40 0 1.018
K092 Kota C P 48 6 1.018
K093 Kota C L 33 1 1.018
K094 Kota C P 32 3 1.018
K095 Kota C P 24 1 1.018
K096 Kota C P 59 1 1.018
K097 Kota C L 35 6 1.018
K098 Kota C L 56 6 1.018
K099 Kota C L 33 2 1.018
K100 Kota C P 23 4 1.018
K101 Kota C P 22 6 1.018
K102 Kota C P 44 4 1.018
K103 Kota C P 29 4 1.018
K104 Kota C P 37 3 1.018
K105 Kota C P 18 3 1.018
K106 Kota C L 58 0 1.018
K107 Kota C L 46 6 1.018
K108 Kota C L 52 5 1.018
K109 Kota C P 55 4 1.018
K110 Kota C L 60 3 1.018
K111 Kota C L 55 6 1.018
K112 Kota C L 39 3 1.018
K113 Kota C L 37 5 1.018
K114 Kota C P 19 3 1.018
K115 Kota C L 40 0 1.018
K116 Kota C L 19 6 1.018
K117 Kota C L 54 5 1.018
K118 Kota C L 23 4 1.018
K119 Kota C P 50 4 1.018
K120 Kota C L 36 2 1.018
K121 Kota C P 58 3 1.018
K122 Kota C L 18 5 1.018
K123 Kota C P 35 4 1.018
K124 Kota C P 44 0 1.018
K125 Kota C P 19 3 1.018
K126 Kota C P 46 3 1.018
K127 Kota C L 18 3 1.018
K128 Kota C L 37 1 1.018
K129 Kota C P 51 1 1.018
K130 Kota C P 34 5 1.018
K131 Kota C L 32 4 1.018
K132 Kota C P 33 6 1.018
K133 Kota C P 35 3 1.018
K134 Kota C P 36 1 1.018
K135 Kota C L 39 5 1.018
K136 Kota C L 48 2 1.018
K137 Kota C L 46 4 1.018
K138 Kota C L 26 4 1.018
K139 Kota C L 25 5 1.018
K140 Kota C P 55 1 1.018
K141 Kota C L 60 5 1.018
K142 Kota C L 34 0 1.018
K143 Kota C P 47 2 1.018
K144 Kota C L 43 5 1.018
K145 Kota C L 59 1 1.018
K146 Kota C P 21 1 1.018
K147 Kota C L 33 1 1.018
K148 Kota C P 28 6 1.018
K149 Kota C L 30 5 1.018
K150 Kota C P 21 1 1.018
K151 Kota C L 38 0 1.018
K152 Kota C P 58 2 1.018
K153 Kota C L 42 5 1.018
K154 Kota C P 18 5 1.018
K155 Kota C P 50 1 1.018
K156 Kota C L 49 4 1.018
K157 Kota C P 54 6 1.018
K158 Kota C P 25 6 1.018
K159 Kota C L 19 2 1.018
K160 Kota C L 24 0 1.018
K161 Kota C P 58 4 1.018
K162 Kota C P 33 0 1.018
K163 Kota C L 38 1 1.018
K164 Kota C P 47 0 1.018
K165 Kota C L 38 0 1.018
K166 Kota C L 44 5 1.018
K167 Kota C P 32 2 1.018
K168 Kota C P 60 5 1.018
K169 Kota C L 27 3 1.018
K170 Kota C L 53 4 1.018
K171 Kota C P 51 6 1.018
K172 Kota C L 49 1 1.018
K173 Kota C P 48 4 1.018
K174 Kota C P 29 2 1.018
K175 Kota C L 21 2 1.018
K176 Kota C P 33 4 1.018
K177 Kota C P 52 3 1.018
K178 Kota C L 23 1 1.018
K179 Kota C L 22 3 1.018
K180 Kota C L 54 0 1.018

A) Identify two types of sampling errors based on this situation.

Given the discrepancies between the intended and actual sample sizes across the three cities, two key types of sampling errors can be identified:

1. Disproportionate Allocation Bias

This error arises when the actual number of respondents per stratum (city) deviates from the planned sample allocation. The intended design was equal allocation (200 respondents per city, totaling 600), yet:

  • City A was over-sampled (250 respondents),
  • City B was severely under-sampled (120 respondents),
  • City C was slightly under-sampled (180 respondents).

Such disproportionality distorts the representativeness of the sample, causing overrepresented strata to exert excessive influence on the survey estimates, and underrepresented strata to be marginalized, thereby introducing systematic bias in population inference.

2. Nonresponse Error

Nonresponse error occurs when selected individuals do not participate in the survey. In this case, the shortfall of 80 respondents in City B and 20 in City C suggests potential nonresponse. This type of error is particularly problematic if the nonrespondents differ significantly from respondents in key characteristics, which could lead to nonrandom bias in the survey outcomes. It not only reduces effective sample size but also jeopardizes the generalizability of findings.

B) How would you calculate weighting adjustments to restore proportional representation?

To restore proportionality and correct sampling imbalances, a weight adjustment procedure is applied. The goal is to reassign statistical influence to each respondent in line with the original design. Steps for Calculating Weight Adjustment:

1. Determine Target Proportion per City

Each city was intended to contribute 200 out of 600 total respondents:

\[\text{Target Proportion} = \frac{200}{600} = 0.3333\]

2. Calculate Actual Proportion from Survey Data

Total actual respondents: 250 (City A) + 120 (City B) + 180 (City C) = 550

  • City A: \(( \frac{250}{550} ≈ 0.4545 )\)
  • City B: \(( \frac{120}{550} ≈ 0.2182 )\)
  • City C: \(( \frac{180}{550} ≈ 0.3273 )\)

3. Compute Weight Adjustment per City

Using the formula:

\[\text{Weight}_{city} = \frac{\text{Target Proportion}}{\text{Actual Proportion}}\]

City Actual Count Actual Proportion Weight
City A 250 0.4545 \(( \frac{0.3333}{0.4545} ≈ 0.733 )\)
City B 120 0.2182 \(( \frac{0.3333}{0.2182} ≈ 1.528 )\)
City C 180 0.3273 \(( \frac{0.3333}{0.3273} ≈ 1.019 )\)

Interpretation and Analytical Implications:

  • Weights below 1 (e.g., City A) indicate down-weighting is needed to reduce overrepresentation.

  • Weights above 1 (e.g., Cities B and C) reflect up-weighting to compensate for underrepresentation.

These adjustments are critical for ensuring statistical estimates reflect the intended sample design, preserving external validity and enhancing the accuracy of population inferences. Weighting is particularly essential in policy-relevant studies to avoid misrepresentation due to sampling imbalances.

Using R:

# Input data
city <- c("City A", "City B", "City C")
actual_count <- c(250, 120, 180)
total_actual <- sum(actual_count)

# Target proportion (equal allocation: 200 per city out of 600)
target_proportion <- 200 / 600  # 0.3333

# Compute actual proportions
actual_proportion <- actual_count / total_actual

# Calculate weight adjustment for each city
weight <- round(target_proportion / actual_proportion, 3)

# Create final result table
result <- data.frame(
  City = city,
  Actual_Count = actual_count,
  Actual_Proportion = round(actual_proportion, 4),
  Weight = weight
)

# Display result using kable
kable(result, caption = "Weighting Adjustments Based on Survey Proportions")
Table 1.1: Weighting Adjustments Based on Survey Proportions
City Actual_Count Actual_Proportion Weight
City A 250 0.4545 0.733
City B 120 0.2182 1.528
City C 180 0.3273 1.019

1.2 Survey Design for Online Motorcycle Taxi User Comfort Perception During Peak Hours

A) Sampling Approach to Capture Representative Perceptions Without Surveying All Day

To capture the perception of comfort from online motorcycle taxi users during peak hours without surveying throughout the entire day, we will use a stratified sampling approach. The survey will focus specifically on two time strata: morning peak hours (07:00–09:00) and evening peak hours (17:00–19:00). The goal is to obtain a representative sample of users in these two critical time periods, ensuring that both time windows are well-represented.

  • Stratified Sampling: This method divides the population into two strata based on time periods (morning and evening). We will select respondents from each stratum proportionally, ensuring that both periods are adequately represented.

  • Sampling without Full-Day Coverage: Instead of conducting a survey over the entire day, we will concentrate on the peak hours only. This allows us to focus our data collection efforts during these critical periods, reducing survey costs and time while still obtaining useful information.

B) Time Design, Respondent Selection Method, and Justification for Sampling Units

Time Design: The survey will be conducted during two defined time windows:

  • Morning Peak: From 07:00 to 09:00
  • Evening Peak: From 17:00 to 19:00

Respondent Selection Method: Simple Random Sampling will be used to select respondents within each time window. This ensures that each user has an equal chance of being selected during these peak hours.

Justification for Sampling Units: The sampling units are individual users of online motorcycle taxis during the peak hours. Since peak hours are when the highest number of users interact with the service, selecting respondents during these periods ensures that the results reflect the perceptions of users who are most likely to experience the challenges and issues associated with peak-hour rides, such as longer wait times, higher fares, or comfort concerns.

C) Adjusting Survey Results Based on Disproportionate Respondent Proportions

Given that 60% of respondents are from the morning session, while 40% are from the evening session, and knowing that historical data shows that the actual user distribution during the evening is twice as large as in the morning (67% evening, 33% morning), we need to adjust the survey results to reflect this discrepancy. Here’s the step-by-step calculation:

Step 1: Calculate Historical Proportions

From historical data:

  • Morning users: 33% (0.33)

  • Evening users: 67% (0.67)

From the survey:

  • Morning respondents: 60% (0.60)

  • Evening respondents: 40% (0.40)

▪▪▪

Step 2: Calculate the Weights for Each Stratum

To adjust for the imbalance in the number of respondents from each stratum, we calculate weights for each time period using the formula:

\[\text{Weight} = \frac{\text{Historical Proportion}}{\text{Proportion of Respondents in the Sample}}\]

✅Weight for Morning Stratum:

\(\text{Weight for Morning} = \frac{0.33}{0.60} = 0.55\)

This means responses from morning users need to be multiplied by 0.55 to adjust them to the actual proportion of users.

✅Weight for Evening Stratum:

\(\text{Weight for Evening} = \frac{0.67}{0.40} = 1.675\)

This means responses from evening users will be multiplied by 1.675 to adjust for the underrepresentation of evening users.

▪▪▪

Step 3: Adjust the Survey Results Using the Weights

Now, let’s assume that the comfort score reported by the respondents for the morning and evening sessions are as follows:

  • Morning respondents report a comfort score of 4.5
  • Evening respondents report a comfort score of 4.2

We apply the weights as follows:

✅Adjusted score for Morning:

\(\text{Adjusted score for Morning} = 4.5 \times 0.55 = 2.475\)

✅Adjusted score for Evening:

\(\text{Adjusted score for Evening} = 4.2 \times 1.675 = 7.035\)

▪▪▪

Step 4: Calculate the Final Weighted Average

The total adjusted score is the sum of the adjusted scores for both groups:

  • \(\text{Total adjusted score} = 2.475 + 7.035 = 9.51\)

Next, calculate the total weight

  • \(\text{Total weight} = 0.55 + 1.675 = 2.225\)

Finally, calculate the weighted average score

  • \(\text{Weighted average score} = \frac{9.51}{2.225} = 4.28\)

Using R:

# Step 1: Define the historical and sample proportions
historical_proportion <- c(0.33, 0.67)  # Morning = 33%, Evening = 67%
survey_proportion <- c(0.60, 0.40)      # Morning respondents = 60%, Evening respondents = 40%

# Step 2: Calculate the weights for each stratum (morning and evening)
weight_morning <- historical_proportion[1] / survey_proportion[1]
weight_evening <- historical_proportion[2] / survey_proportion[2]

# Display weights
cat("Weight for Morning: ", weight_morning, "\n")
## Weight for Morning:  0.55
cat("Weight for Evening: ", weight_evening, "\n")
## Weight for Evening:  1.675
# Step 3: Define the comfort scores reported by respondents
comfort_score_morning <- 4.5
comfort_score_evening <- 4.2

# Step 4: Adjust the comfort scores using the weights
adjusted_score_morning <- comfort_score_morning * weight_morning
adjusted_score_evening <- comfort_score_evening * weight_evening

# Display the adjusted scores
cat("Adjusted Score for Morning: ", adjusted_score_morning, "\n")
## Adjusted Score for Morning:  2.475
cat("Adjusted Score for Evening: ", adjusted_score_evening, "\n")
## Adjusted Score for Evening:  7.035
# Step 5: Calculate the total adjusted score and the weighted average score
total_adjusted_score <- adjusted_score_morning + adjusted_score_evening
total_weight <- weight_morning + weight_evening
weighted_average_score <- total_adjusted_score / total_weight

# Display the weighted average score
cat("Total Adjusted Score: ", total_adjusted_score, "\n")
## Total Adjusted Score:  9.51
cat("Total Weight: ", total_weight, "\n")
## Total Weight:  2.225
cat("Weighted Average Score: ", weighted_average_score, "\n")
## Weighted Average Score:  4.274157
# Creating a summary table with the results
result <- data.frame(
  Time_Period = c("Morning", "Evening"),
  Respondent_Proportion = survey_proportion,
  Historical_Proportion = historical_proportion,
  Weight = c(weight_morning, weight_evening),
  Comfort_Score = c(comfort_score_morning, comfort_score_evening),
  Adjusted_Score = c(adjusted_score_morning, adjusted_score_evening)
)

# Display result using kable
library(knitr)
kable(result, caption = "Adjusted Comfort Scores with Weights for Each Stratum")
Table 1.2: Adjusted Comfort Scores with Weights for Each Stratum
Time_Period Respondent_Proportion Historical_Proportion Weight Comfort_Score Adjusted_Score
Morning 0.6 0.33 0.550 4.5 2.475
Evening 0.4 0.67 1.675 4.2 7.035

1.3 Designing a Student Satisfaction Survey on Academic Services

You have been assigned by the university academic office to design a survey instrument aimed at evaluating student satisfaction with academic services, which include: online course registration (KRS Online), academic advising, administrative services, access to academic information, and academic support services.

The research team requests you to:

  • Design 25 core survey questions with varied scales and formats.

  • Develop a validation system for the instrument.

  • Determine the distribution method and conduct statistical testing of the questionnaire.

  • Prepare a simulation of sampling strategy and preliminary data processing.

1.3.1 Questionnaire Design

25 main questions representing the 5 aspects of academic services:

  1. Online Course Registration (KRS Online)

  2. Academic Advising

  3. Administrative Services

  4. Access to Academic Information

  5. Study Completion Assistance

Link Questionnaire

1.3.2 Validation Scheme

Study Program Semester Overall Satisfaction Gender
1 Petroleum Engineering Semester 6 7/10 Male
5 Petroleum Engineering Semester 1 9/10 Female
8 Petroleum Engineering Semester 6 9/10 Female
6 Petroleum Engineering Semester 8 9/10 Female
2 Petroleum Engineering Semester 3 1/10 Female
4 Petroleum Engineering Semester 1 3/10 Male
3 Petroleum Engineering Semester 7 6/10 Female
7 Petroleum Engineering Semester 8 4/10 Female
16 Product Design Semester 3 6/10 Male
15 Product Design Semester 7 10/10 Female

1.3.2.1 Content Validation

Content validation ensures that the survey data is accurate, complete, and logically structured according to the intended purpose of each variable.

A) Structure and data Type Validation

This step verifies that each variable is stored in the appropriate data type and follows the predefined input format. This is critical to prevent errors in analysis due to incorrect data formats.

Variable Expected Format/Type Validation Purpose
Respondent_ID String (unique identifier) Ensures no duplication of responses and enables traceability. Checked using duplicated() to ensure each response is from a unique participant.
Study_Program Categorical (factor) Should match a predefined list of academic programs. Ensures category integrity and allows valid grouping during analysis.
Gender Fixed Category Limited to “Male” or “Female” to ensure consistency. Inconsistent entries (like “F” or lowercase “female”) are standardized.
Current_Semester Integer (1–14) Ensures that responses are within plausible academic progression. Semester values beyond this range indicate input error or fake data.
Academic_Service_Satisfaction Integer Scale (1–5) Part of a Likert scale. Ensures valid values are used (1 = Very Dissatisfied, …, 5 = Very Satisfied).
Overall_Satisfaction Integer Scale (1–10) Serves as a summary perception. Must be in the 1–10 range to maintain rating integrity.

Why it matters: Ensures compatibility with statistical functions and guards against data corruption during collection or manual entry.

▪▪▪

B) Compltenes Validation

Checks if every mandatory field has been filled in. Missing data (NA/null values) can skew analysis, especially in small samples.

✅How it’s done:

  colSums(is.na(data))
##        Study_Program     Current_Semester Overall_Satisfaction 
##                    0                    0                    0 
##               Gender 
##                    0

✅ Action if missing values are found:

  • For critical variables (e.g., satisfaction ratings), rows are removed.

  • For non-critical metadata, missing values may be imputed or flagged.

Why it matters: Analysis relying on incomplete cases may lead to biased or misleading conclusions.

▪▪▪

C) Logical Consistency Check

Evaluates if values make sense when viewed in relation to other variables.

  • Example:

    • A first-semester student** giving a very high score for “Overall Satisfaction” while also giving the lowest score to academic services might indicate misunderstanding or careless answering.

    • If a participant claims to be in semester 20, this is likely an error since most academic programs do not exceed 14 semesters.

Why it matters: Ensures the internal logic of responses aligns with reality, preventing garbage-in-garbage-out issues during analysis.

▪▪▪

D) Category Label Consistency

Ensures that categorical entries are consistently labeled. Inconsistent labels (e.g., “f”, “FEMALE”, “F”) are cleaned and standardized.

  • Standardization code:
   data$Gender <- ifelse(tolower(data$Gender) == "f", "Female", "Male")

Why it matters: Prevents splitting of categories during group-wise analysis and ensures valid grouping for charts, summaries, or modeling.

1.3.2.2 Statistical Validation

Statistical validation checks whether the data meaningfully supports the constructs being measured and whether the instrument is reliable and valid statistically.

A) Construct Validity Determines whether the variable relationships align with theoretical expectations.

  • Example: Students satisfied with academic services are expected to be satisfied overall.

  • Method: Use correlation analysis between Academic_Service_Satisfaction and Overall_Satisfaction

  • Interpretation:

    • Correlation > 0.4: acceptable

    • Correlation > 0.6: strong

    • < 0.3: reevaluate if the items truly represent the construct

Why it matters: Confirms whether each variable accurately reflects the underlying dimension it intends to measure.

B) Reliability Testing Used when multiple questions are asked to measure a single concept.

  • Measures internal consistency between those items.

  • Most common method: Cronbach’s Alpha

  • Rule of thumb:

    • α ≥ 0.7: acceptable
    • α ≥ 0.8: good
    • α < 0.7: potentially unreliable

{r, message=FALSE, warning=FALSE, echo=TRUE} Install dan load package psych install.packages(“psych”) library(psych)

Misalnya data responden terhadap 5 item (pertanyaan) dalam bentuk data frame data <- data.frame( item1 = c(4, 3, 5, 4, 2), item2 = c(4, 4, 4, 5, 3), item3 = c(5, 5, 4, 4, 4), item4 = c(3, 3, 3, 2, 4), item5 = c(4, 4, 4, 5, 5) )

Menghitung Cronbach’s Alpha alpha_result <- psych::alpha(data)

Melihat hasilnya alpha_result\(total\)raw_alpha

Why it matters: Ensures the survey instrument provides consistent results across items measuring the same construct.

C) Outlier Detection and Distribution Analysis Ensures the data is not heavily skewed and doesn’t contain extreme anomalies.

  • Visualized via:

    boxplot(data$Overall_Satisfaction)

    hist(data$Academic_Service_Satisfaction)

  • Detects response bias (e.g., everyone picking 10 or 5), which may indicate social desirability or misunderstanding.

Why it matters: Outliers can disproportionately influence statistical analysis, especially with small sample sizes.

1.3.2.3 Adjustment Based on Validation Results

Based on validation outputs, these are common follow-up actions:

Issue Identified Action Taken
Duplicate Respondent_IDs Remove duplicate entries
Invalid entries in Study_Program Replace or remove non-matching entries
Mislabeling in Gender Standardize all categories
Out-of-range values Remove or correct based on logical rules
Missing responses in key variables Remove or impute depending on criticality
Weak correlation between key constructs Consider rewording survey items for clarity
Low internal consistency (Cronbach < 0.7) Merge/rephrase redundant or ambiguous items

batas yang belum di publish sebelum dinilai T-T

1.3.3 Distribution and Sampling Strategy

A well-planned distribution strategy ensures that the survey reaches the intended target respondents effectively, increases response rates, and maintains data quality. In this study, the distribution strategy includes:

A) Platform and Delivery

✅Medium Used: The questionnaire is distributed online via Google Forms, considering its accessibility, ease of use, and integration with spreadsheets for data handling.

✅ Access: The survey link is shared through official university communication channels, such as:

  • Academic WhatsApp or LINE groups by cohort or department

  • University mailing list

  • Student portals or LMS (Learning Management Systems)

B) Timing

The survey is open for 7 days to allow ample response time while maintaining urgency. Reminders are sent on Day 3 and Day 6 to improve response rates.

C) Incentive (optional)

Optionally, non-monetary incentives such as e-certificates or point contributions to student activity units (SKKM) may be offered to encourage participation.

1.3.4 Sampling Strategy

To ensure representation across diverse student segments, a Stratified Random Sampling approach is used. This helps maintain proportional representation based on relevant strata, improving generalizability of results.

A) Population

The population includes all active undergraduate students in the university during the current academic semester.

B) The sample is stratified based on:

This stratification ensures balanced input across academic experiences and program characteristics.

  • Study Program

  • Current Semester

  • (Optional) Gender

C) Sample Size Determination

Total desired sample: 200 respondents

Proportional allocation across study programs is calculated using:

\(n_i = \left( \frac{N_i}{N} \right) \times n\)

where \(( n_i )\) = sample from stratum i,

\(( N_i )\) = population of stratum i,

\(( N )\) = total population,

and \(( n )\) = total sample size (200)

D) Sampling Execution

Within each stratum, respondents are randomly selected using the sample() function in R. Sampling is without replacement to prevent duplicate responses.

E) Non-Response Handling

Oversampling is considered in strata with historically low response rates. Reminders and targeted outreach ensure participation from underrepresented groups.

1.3.5 Simulated Data and Preliminary Analysis

To anticipate and demonstrate how the collected data can be utilized, a simulated dataset was created and subjected to basic exploratory analysis. This step is essential for testing the survey design, data structure, and potential analytical paths prior to actual data collection.

1.3.5.1 Data Simulation Overview

A total of 200 simulated responses were generated to reflect plausible patterns of student feedback. The variables include:

  • Study Program

  • Current Semester

  • Gender

  • Satisfaction Indicators, such as:

    • Academic Service Satisfaction

    • Lecturer Performance

    • Facilities & Infrastructure

    • Overall Satisfaction

  • Open-Ended Feedback (optional text field)

All numerical satisfaction responses were simulated on a 1–10 Likert-type scale, consistent with the questionnaire format.

ID Responden Gender Program Studi Semester Status Mahasiswa Jenis Pembiayaan Akses KRS Error Teknis KRS Tampilan KRS Bantuan KRS Respon Dosen Wali Frekuensi Temu Dosen Wali Kejelasan Arahan Dosen Wali Pemahaman Dosen Wali Kecepatan Layanan Admin Profesionalitas Staf Kemudahan Dokumen Sumber Info Akademik Ketepatan Waktu Info Akses Regulasi Akademik Kepuasan Keseluruhan Pernah Minta Dokumen Pernah Telat karena Info Cek Portal Rutin Pernah Ikut Remedial Tahu Tempat Bantuan Saran
R001 Female Pulp and Paper Processing Technology Semester 5 Regular Class Scholarship 1 9 2 5 3 None 4 No Slow 2 Very Convenient Academic Advisor Late 4 2 Yes No Yes No No Extend KRS deadlines
R002 Male Pulp and Paper Processing Technology Semester 3 Employee Class Scholarship 4 3 1 1 4 3-4 times 1 No Very Fast 2 Convenient Bulletin Boards Very Late 2 1 Yes Yes Yes Yes No Faster transcript processing
R003 Male Palm Oil Processing Technology Semester 5 Regular Class Self-funded 3 6 3 4 1 None 2 Yes Slow 1 Convenient Academic Portal On time 4 6 Yes No Yes No Yes Faster transcript processing
R004 Male Regional and City Planning Final Year Employee Class Other 5 6 4 4 3 1-2 times 5 No Very Slow 1 Very Inconvenient WhatsApp / Telegram Groups Late 2 6 No Yes Yes No Yes Faster transcript processing
R005 Female Petroleum Engineering Semester 8 Employee Class Self-funded 2 4 3 4 4 None 3 Yes Slow 4 Very Inconvenient University Website Very Timely 2 10 No No No Yes No Fix portal bugs
R006 Female Mining Engineering Semester 2 Employee Class Scholarship 2 4 1 5 1 More than 4 times 2 Yes Very Slow 5 Very Convenient Bulletin Boards Late 4 4 No No No No No Improve advisor availability
R007 Female Petroleum Engineering Semester 1 Regular Class Self-funded 1 4 5 3 4 More than 4 times 5 Yes Neutral 4 Inconvenient Bulletin Boards Very Late 5 8 No Yes Yes No No Faster transcript processing
R008 Male Civil Engineering Semester 6 Employee Class Self-funded 1 4 3 5 1 More than 4 times 3 Yes Fast 1 Inconvenient University Website Timely 4 10 No No No No No More communication on updates
R009 Male Metallurgical Engineering Semester 7 Regular Class Self-funded 5 2 1 1 3 3-4 times 4 Yes Fast 5 Very Convenient Other Very Timely 5 4 No Yes Yes Yes Yes None
R010 Male Pulp and Paper Processing Technology Semester 4 Regular Class Self-funded 3 6 3 1 5 1-2 times 4 No Fast 2 Very Inconvenient Academic Advisor Very Timely 3 5 Yes Yes No Yes Yes Extend KRS deadlines