If, there exist multiple groups, then a researcher would use analysis of variance
or multivariate analysis of variance (ANOVA/MANOVA). Again the nonparametric equivalents to this method are the Kruskal-Wallis analysis of ranks and the Median test. This is what is termed differences between independent groups (Tabachnick & Fidell, 2001).
Alternatively, differences between dependent groups arise if a researcher wants to compare two variables measured in the same sample, in this regard, a researcher would customarily use the t-test for dependent samples . Nonparametric alternatives to this test are the Sign test and Wilcoxon's matched pairs test (cf. section 3.2 for such application). However, if the variables of interest are dichotomous in nature (for instance “pass” or “fail”), then McNemar's chi-square test is appropriate.
..
If there are more than two variables that were measured in the same sample, then a researcher would customarily use repeated measures ANOVA. Nonparametric alternatives to this method are Friedman's two-way analysis of variance and Cochran Q test (if the variable was measured in terms of categories for instance “passed” or “failed”). Noting that Cochran Q is particularly useful for measuring changes in frequencies (proportions) across time.
In addition to the above test or analysis technique for significant levels, there are other three types of commonly used nonparametric correlation coefficients, which are used to test relationship between variables. These include (1) Spearman R (2) Kendall Tau and (3) Gamma coefficient; these would be explained shortly. Noting that chi-square statistic computed for two-way frequency tables, also provides a careful measure of a relation between two (tabulated) variables, and unlike the correlation measures listed, it could be used for variables that are measured on a nominal scale (Tabachnick & Fidell, 2001).
With reference to NPA correlation measures such as Spearman R, it assumes that the variables under consideration were measured on at least an ordinal (rank order) scale that is, individual observations can be ranked into two ordered series. Spearman R could be thought of as the regular pearson product moment correlation coefficient, that is, in terms of proportion of variability accounted for, except that Spearman R is computed from ranks (Tabachnick & Fidell, 2001).
Kendall Tau is equivalent to Spearman R with regard to the underlying assumptions. It is also comparable in terms of its statistical power. However, Spearman R and Kendall Tau are usually not identical in magnitude because their underlying logic as well as their computational formulas are very different.
In basic statistics for example, if one wants to compare students' math skills at the beginning of the semester with their skills at the end of the semester.
Application of Non-Parametric and Parametric Analysis amongst Postgraduate Education Research in South Africa: A Survey of Three South African Universities
98
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88 |
Page 89 |
Page 90 |
Page 91 |
Page 92 |
Page 93 |
Page 94 |
Page 95 |
Page 96 |
Page 97 |
Page 98 |
Page 99 |
Page 100 |
Page 101 |
Page 102 |
Page 103 |
Page 104 |
Page 105 |
Page 106 |
Page 107 |
Page 108 |
Page 109 |
Page 110 |
Page 111 |
Page 112 |
Page 113 |
Page 114 |
Page 115 |
Page 116 |
Page 117 |
Page 118 |
Page 119 |
Page 120 |
Page 121 |
Page 122 |
Page 123 |
Page 124 |
Page 125 |
Page 126 |
Page 127 |
Page 128 |
Page 129 |
Page 130 |
Page 131 |
Page 132 |
Page 133 |
Page 134 |
Page 135 |
Page 136 |
Page 137 |
Page 138 |
Page 139 |
Page 140 |
Page 141 |
Page 142 |
Page 143 |
Page 144 |
Page 145 |
Page 146 |
Page 147 |
Page 148 |
Page 149 |
Page 150 |
Page 151 |
Page 152 |
Page 153 |
Page 154 |
Page 155 |
Page 156 |
Page 157 |
Page 158 |
Page 159 |
Page 160 |
Page 161 |
Page 162 |
Page 163 |
Page 164 |
Page 165 |
Page 166 |
Page 167 |
Page 168 |
Page 169 |
Page 170 |
Page 171 |
Page 172 |
Page 173 |
Page 174 |
Page 175 |
Page 176 |
Page 177 |
Page 178 |
Page 179 |
Page 180 |
Page 181 |
Page 182 |
Page 183 |
Page 184 |
Page 185 |
Page 186 |
Page 187 |
Page 188 |
Page 189 |
Page 190 |
Page 191 |
Page 192 |
Page 193 |
Page 194 |
Page 195 |
Page 196 |
Page 197 |
Page 198 |
Page 199 |
Page 200 |
Page 201 |
Page 202 |
Page 203 |
Page 204 |
Page 205 |
Page 206 |
Page 207 |
Page 208 |
Page 209 |
Page 210 |
Page 211 |
Page 212 |
Page 213 |
Page 214 |
Page 215 |
Page 216 |
Page 217 |
Page 218 |
Page 219 |
Page 220 |
Page 221 |
Page 222 |
Page 223 |
Page 224 |
Page 225 |
Page 226 |
Page 227 |
Page 228 |
Page 229 |
Page 230 |
Page 231 |
Page 232 |
Page 233 |
Page 234 |
Page 235 |
Page 236 |
Page 237 |
Page 238 |
Page 239 |
Page 240 |
Page 241 |
Page 242 |
Page 243 |
Page 244 |
Page 245 |
Page 246 |
Page 247 |
Page 248 |
Page 249 |
Page 250 |
Page 251 |
Page 252 |
Page 253 |
Page 254 |
Page 255 |
Page 256 |
Page 257 |
Page 258 |
Page 259 |
Page 260 |
Page 261 |
Page 262 |
Page 263 |
Page 264 |
Page 265 |
Page 266 |
Page 267 |
Page 268 |
Page 269 |
Page 270 |
Page 271 |
Page 272 |
Page 273 |
Page 274 |
Page 275 |
Page 276 |
Page 277 |
Page 278 |
Page 279 |
Page 280 |
Page 281 |
Page 282 |
Page 283 |
Page 284 |
Page 285 |
Page 286 |
Page 287 |
Page 288 |
Page 289 |
Page 290 |
Page 291 |
Page 292 |
Page 293 |
Page 294 |
Page 295 |
Page 296 |
Page 297 |
Page 298 |
Page 299 |
Page 300 |
Page 301 |
Page 302 |
Page 303 |
Page 304 |
Page 305 |
Page 306 |
Page 307 |
Page 308 |
Page 309 |
Page 310 |
Page 311 |
Page 312 |
Page 313 |
Page 314 |
Page 315 |
Page 316 |
Page 317 |
Page 318 |
Page 319 |
Page 320 |
Page 321 |
Page 322 |
Page 323 |
Page 324 |
Page 325 |
Page 326 |
Page 327 |
Page 328 |
Page 329 |
Page 330 |
Page 331 |
Page 332 |
Page 333 |
Page 334 |
Page 335 |
Page 336 |
Page 337 |
Page 338 |
Page 339 |
Page 340 |
Page 341 |
Page 342 |
Page 343 |
Page 344 |
Page 345 |
Page 346 |
Page 347 |
Page 348 |
Page 349 |
Page 350 |
Page 351 |
Page 352 |
Page 353 |
Page 354 |
Page 355 |
Page 356 |
Page 357 |
Page 358 |
Page 359 |
Page 360 |
Page 361 |
Page 362 |
Page 363 |
Page 364 |
Page 365 |
Page 366 |
Page 367 |
Page 368 |
Page 369 |
Page 370 |
Page 371 |
Page 372 |
Page 373 |
Page 374 |
Page 375 |
Page 376 |
Page 377 |
Page 378 |
Page 379 |
Page 380 |
Page 381 |
Page 382 |
Page 383 |
Page 384 |
Page 385 |
Page 386 |
Page 387 |
Page 388 |
Page 389 |
Page 390 |
Page 391 |
Page 392 |
Page 393 |
Page 394 |
Page 395 |
Page 396 |
Page 397 |
Page 398 |
Page 399 |
Page 400 |
Page 401 |
Page 402 |
Page 403 |
Page 404 |
Page 405 |
Page 406 |
Page 407 |
Page 408 |
Page 409 |
Page 410 |
Page 411 |
Page 412 |
Page 413 |
Page 414 |
Page 415 |
Page 416 |
Page 417 |
Page 418 |
Page 419 |
Page 420 |
Page 421 |
Page 422 |
Page 423 |
Page 424 |
Page 425 |
Page 426 |
Page 427 |
Page 428 |
Page 429 |
Page 430 |
Page 431 |
Page 432 |
Page 433 |
Page 434 |
Page 435 |
Page 436 |
Page 437 |
Page 438 |
Page 439 |
Page 440 |
Page 441 |
Page 442 |
Page 443 |
Page 444 |
Page 445 |
Page 446 |
Page 447 |
Page 448 |
Page 449 |
Page 450 |
Page 451 |
Page 452 |
Page 453 |
Page 454