Index
A
a priori ordering, 348
absolute addressing (Excel), extending semipartials, 332–335
adjusted group means and effect coding, 386–388
adjusting means, 381–386
calculating, 270–271
manipulating, 221–223
setting the level, 204
alternative hypotheses, 116, 198–199
analysis
ANOVA, 261
F tests, 268–270
scores, partitioning, 261–264
of dependent group t-test, 249–252
The Analysis of Variance and Alternatives (Wiley, 1980), 372
ANCOVA (analysis of covariance), 361
bias, removing, 375–379
common regression line, testing for, 372–375
effect coding, adjusted group means, 386–388
means, adjusting with LINEST() function, 381–386
multiple comparisons
planned contrasts, 394–395
Scheffe method, 389–393
multiple covariance, 396–398
purpose of
bias reduction, 362–363
greater power, 362
statistical power, increasing, 363
versus ANOVA, 363–365
covariate, adding to analysis, 365–372
ANOVA (analysis of variance), 261. See also factorial ANOVA
alpha, calculating, 270–271
F distribution, 274–275
calculated F, comparing to critical F, 270
noncentral F, 305
noncentrality parameters, 306
factorial ANOVA, 287–291
interaction, 293–294
main effect, calculating, 296–300
statistical significance of, 294–295
main effects, 294–295
multiple comparison procedures, 277–278
planned orthogonal contrasts, 283–286
Scheffe procedure, 278–283
and multiple regression, 308–309
effect coding, 310–312
replication, 303
scores, partitioning, 261–262
sum of squares between groups, 263, 266–268
sum of squares within groups, 263–265
Single Factor ANOVA tool (Excel), 322–323
unequal group sizes, 275–277
variance estimates, 315–316
ANOVA: Single Factor tool (Data Analysis add-in), 269–270
ANOVA: Two-Factor with Replication tool (Data Analysis add-in), 291, 293
design cells, 291–292
limitations of, 304–305
ANOVA: Two-Factor without Replication tool (Data Analysis add-in), 303–304
arguments, 38–39
Tails (T.TEST() function), 240–245
Type (T.TEST() function), 245
independent observations, 245–247
standard error, calculating for dependent groups, 247–251
arrays, identifying in T.TEST() function, 239–240
assigning effect codes in Excel, 319–322
assumptions, making
BINOM.INV() function, 124–127
binomial distribution formula, 122–124
hypothesis testing, 127–128
independent selections, 122
random selection, 120–122
AVERAGE() function, 37
B
balanced designs, 300–301
correlation matrices, 339
order of entry, 340–342
Behrens-Fisher problem, 140, 276
bell curve. See normal distribution
between group variance, calculating, 266–268
bias reduction, ANCOVA, 362–363, 375–379
BINOM.DIST() function, 117–119
comparing with BINOM.INV() function, 128–129
BINOM.INV() function, 124–127
binomial distribution formula, 122–124
comparing with BINOM.DIST() function, 128–129
bins, 26
building frequency distributions, 25
FREQUENCY() function, 26–28
with pivot tables, 28–31
simulated frequency distributions, 31–32
C
calculated F, comparing to critical F, 270
calculating
alpha, 270–271
correlation, 81–86
CORREL() function, 86–89
Correlation tool (Data Analysis add-in), 91–93
median, 46–48
mode, 48–50
standard deviation, 68–70
variance
within group, 264–265
between group, 266–268
capitalizing on chance, 120, 260
category scales, 12–14
causation versus correlation, 93–95
cells, design cells, 291–292
Central Limit Theorem, 191–195
central tendency, 36
characteristics of normal distribution, 169–170
kurtosis, 172–174
skewness, 170–172
creating, testing means, 209–212
means, testing, 206
XY charts, 18–19
chi-square distributions, 135–139
CHIDIST() function, 142–144
CHIINV() function, 145
CHISQ.DIST() function, 141–142
CHISQ.DIST.RT() function, 142–144
CHISQ.INV() function, 137–139, 144–145
CHISQ.INV.RT() function, 145
CHISQ.TEST() function, 134–135, 145–147
CHITEST() function, 145–147
CHIDIST() function, 142–144
CHIINV() function, 145
CHISQ.DIST() function, 141–142
CHISQ.DIST.RT() function, 142–144
CHISQ.INV() function, 137–139, 144–145
CHISQ.INV.RT() function, 145
CHISQ.TEST() function, 134–135, 145–147
CHITEST() function, 145–147
Cochran, William, 152
coding
dummy coding, 312
adjusted group means, 386–388
codes, assigning in Excel, 319–322
factorial designs, 324–325
group codes, 311–312
means, adjusting, 381–386
orthogonal coding, 312
coefficient of determination, 109–110
common regression line, testing for (ANCOVA), 372–375
comparing
BINOM.INV() and BINOM.DIST() functions, 128–129
calculated F to critical F, 270
correlation and causation, 93–95
comparison procedures, 277–278
planned orthogonal contrasts, 283–286
Scheffe procedure, 278–283
compatibility functions, 76
CONFIDENCE() function, 186–188
confidence interval, 180–181
constructing, 182–185
CONFIDENCE() function, 186–188
CONFIDENCE.NORM() function, 186–188
CONFIDENCE.T() function, 188–189
Descriptive Statistics tool (Data Analysis add-in), 189–191
hypothesis testing, 191
CONFIDENCE.NORM() function, 186–188
CONFIDENCE.T() function, 188–189
consistency functions, 76
constraints, 75
constructing confidence interval, 182–185
CONFIDENCE() function, 186–188
CONFIDENCE.NORM() function, 186–188
CONFIDENCE.T() function, 188–189
context for inferential statistics, 151–152
internal validity, 152–156
contingency tables, 130
contrast coefficients, 280
calculating, 81–86
versus causation, 93–95
CORREL() function, 86–89
correlation coefficient, 80
covariance, 97
multiple regression
best combination, 105–108
TREND() function, 104–105
partial correlation, 327
regression, 95–96, 98, 101–104
semipartial correlation, 326–327
extending with absolute/relative addressing (Excel), 332–335
sum of squares, achieving with squared semipartial, 327–328
TREND() function, 328–332
TREND() function, 99–101
Correlation tool (Data Analysis add-in), 91–93
counting values with array formula, 53–55
ANCOVA, 361
bias, removing, 375–379
common regression line, testing for, 372–375
purpose of, bias
reduction, 362–363
purpose of, greater power, 362
statistical power, increasing, 363–372
calculating, 82
multiple covariance, 396–398
covariate adding to ANCOVA analysis, 365–372
covariate total sum of squares, 386
creating
charts, testing means, 206–212
one-way pivot tables, 114–116
critical values, 236
calculating with T.INV() function, 232–234
comparing, 218
finding for t-tests, 217–218
finding for z-tests, 216–217
D
Data Analysis add-in tools, 89–91
ANOVA: Single Factor tool, 269–270
ANOVA: Two-Factor with Replication tool, 291, 293
design cells, 291–292
limitations of, 304–305
ANOVA: Two-Factor without Replication tool, 303–304
Correlation tool, 91–93
dependent group t-tests, performing
Equal Variances t-Test tool, 252–254
Unequal Variances t-Test tool, 255–256
Descriptive Statistics tool, 189–191
F-Test Two-Sample for Variances tool, 156–167
T-Test Paired Two Sample for Means tool, 237
T-Test: Two-Sample Assuming Unequal Variances tool, 239
De Moivre, Abraham, 23
decision rule, defining for t-tests, 215–216
defining decision rule for t-tests, 215–216
degrees of freedom, 73–75, 236
in two-test groups, 236
dependent group t-tests, performing with Data Analysis add-in tools, 249–256
descriptive statistics, 22–23
Descriptive Statistics tool (Data Analysis add-in), 189–191
design cells, 291–292
directional hypotheses, 165–167, 226–228
verifying with t-test, 228–234
distributions, t-distribution, 214
documentation (Excel), problems with, 149–151
dummy coding, 312
E
adjusted group means, 386–388
codes, assigning in Excel, 319–322
factorial designs, 324–325
general principles, 310
group codes, 311–312
means, adjusting, 381–386
Equal Variances t-Test tool (Data Analysis add-in), 252–254
error rates
alpha, manipulating, 221–223
beta, 220
establishing internal validity, 152–153
estimates of variance
via ANOVA, 315–316
via regression, 316–317
estimators, 74
Excel
Data Analysis add-in tools. See Data Analysis add-in tools
documentation, problems with, 149–151
effect codes, assigning, 319–322
formula evaluation tool, 56–59
formulas. See formulas
functions. See functions
matrix functions, 110–112
pivot tables
Index display, 147–148
Single Factor ANOVA tool, 322–323
Solver, 42–43
installing, 43
worksheets, setting up, 44–46
experimental designs, multiple regression, 345–348
experiments, managing unequal group sizes, 355–356
F
F ratio, 269
calculated F, comparing to critical F, 270
multiple comparison procedures, 277–278
planned orthogonal contrasts, 283–286
Scheffe procedure, 278–283
noncentral F, 305
noncentrality parameters, 306
factorial ANOVA, 287–288
F tests, 305
noncentral F, 305
noncentrality parameters, 306
fixed factors, 306
interaction, 293–294
main effect, calculating, 296–300
statistical significance of, 294–295
multiple factors, 288–291
random factors, 306
unequal group sizes, 300–303
factors
main effect, calculating, 296–300
statistical significance of, 294–295
mixed models, 306
F.DIST() function, 71–272
FDIST() function, 272
F.DIST.RT() function, 163–164, 272
fields, 9
F.INV() function, 163, 273–274
FINV() function, 273–274
fixed factors, 306
fluctuating proportions of variance, 344–345
formula evaluation tool, 56–59
array formulas, 55–56
values, counting, 53–55
binomial distribution, 122–124
degrees of freedom, 73–75
mode, calculating, 53
regression, 101–104
symbols used in, 71–72
frequency distributions, 19–20
building, 25
FREQUENCY() function, 26–28
with pivot tables, 28–31
descriptive statistics, 22–23
inferential statistics, 23–25
positively skewed, 21–22
simulated frequency distributions, building, 31–32
standard deviation, 65–68
calculating, 68–70
FREQUENCY() function, 26–28
F-Test Two-Sample for Variances tool, 156–167
arguments, 38–39
AVERAGE(), 37
BINOM.DIST(), 117–119
BINOM.INV(), 124–127
CHIDIST(), 142–144
CHIINV(), 145
CHISQ.DIST(), 141–142
CHISQ.DIST.RT(), 142–144
CHISQ.INV.RT(), 145
CHISQ.TEST(), 134–135, 145–147
CHITEST(), 145–147
compatibility functions, 76
CONFIDENCE.T(), 188–189
consistency functions, 76
F.DIST(), 271–272
FDIST(), 272
FINV(), 273–274
FREQUENCY(), 26–28
IF(), 56
INTERCEPT(), 102–104
LINEST(), 102–104
means, adjusting, 381–386
multiple regression, 106–108
multiple regression statistics, 348–354
MATCH(), 53
MEDIAN(), 47
MMULT(), 111–112
MODE(), 48–53
cumulative probability, requesting, 176
point estimate, requesting, 177
NORM.INV(), 177–179
NORM.S.DIST(), 179–180
NORM.S.INV(), 180
returning the result, 39–40
SLOPE(), 102–104
STDEV(), 75
STDEVA(), 76
STDEVP(), 75
STDEV.P() function, 76
STDEV.S() function, 76
STEVPA(), 76
T.DIST(), 234–235
T.DIST.2T(), 235
T.DIST.RT(), 235
multiple regression, 104–106
residuals, 330–332
T-TEST(), 236–238
arrays, identifying, 239–240
Tails argument, 240–245
Type argument, 245–249
VARA(), 76
VARP(), 76
VAR.P(), 77
VARPA(), 77
VAR.S(), 77
G
Galton, Francis, 95
General Linear Model, effect coding, 317–319
group codes, 311–312
groups, unequal sizes, 275–277
H
headers, 10
homogeneity of regression coefficients, 372
How to Lie with Statistics, 149
Huff, Darrell, 149
Huitema, B.E., 372
hypotheses
alternative, 116
directional, 226–227
verifying with t-test, 228–234
nondirectional hypotheses, 226
null hypotheses, 116
I
identifying arrays in T.TEST() function, 239–240
IF() function, 56
independent events, 132–133
independent selections, making assumptions, 122
Index display (pivot tables), 147–148
inferential statistics, 22–25
context for, 151–152
internal validity, 152–156
estimators, 74
influences on statistical power, 257
installing Solver, 43
main effect, calculating, 296–300
statistical significance of, 294–295
intercept, 350
INTERCEPT() function, 102–104
internal validity, 152–153
threats to
chance, 156
history, 153–154
instrumentation, 154
maturation, 154
mortality, 155
regression, 154
selection, 153
testing, 154
interval scales, 15
interval values, distinguishing from text values, 15–17
J-K-L
The Johnson-Neyman Technique, Its Theory and Application (Biometrika, December 1950), 372
Kish, Leslie, 152
kurtosis as characteristic of normal distribution, 172–174
least squares criterion, 18, 42, 45
leptokurtic curve, 173
limitations of ANOVA: Two Factor with Replication tool, 304–305
LINEST() function, 102–104
multiple regression, 106–108
multiple regression statistics, 348–354
lists, 10–11
M
main diagonal, 339
main effects, 294–295
making assumptions
BINOM.INV() function, 124–127
binomial distribution formula, 122–124
hypothesis testing, 127–128
independent selections, 122
random selection, 120–122
managing unequal group sizes
in observational research, 356–359
in true experiments, 355–356
manipulating error rates, 221–223
MATCH() function, 53
matrix functions (Excel), 110–112
mean, 35
adjusting, 381–386
least squares criterion, 45
minimizing the spread, 41–43
charts, creating, 206–212
standard error of the mean, 202–205
statistical power, 219–220
t-test, 213–216
z-test, 199–201
mean deviation, 70–71
mean square between, calculating, 266–268
mean square within, calculating, 265
measuring variability with range, 62–64
median, 35
calculating, 46–48
MEDIAN() function, 47
mesokurtic curve, 173
mixed models, 306
MMULT() function, 111–112
mode, calculating, 48–49
with formulas, 53
with pivot tables, 50–52
MODE() function, 48–53
multiple comparisons, 261, 277–278
planned contrasts, 394–395
planned orthogonal contrasts, 283–286
Scheffe method, 278–283, 389–393
multiple covariance, 396–398
multiple regression
and ANOVA, 308–312
best combination, 105–106
effect coding, factorial designs, 324–325
experimental designs, 345–348
LINEST() function, 348–354
proportions of variance, 312–315
TREND() function, 104–105
unbalanced factorial designs, solving, 337–338
correlation matrices, 339–340
fluctuating proportions of variance, 344–345
order of entry, 340–344
unequal group sizes, managing
in observational research, 356–359
in true experiments, 355–356
N
negative correlation, 79
negatively skewed frequency distributions, 21
noncentrality parameters, 306
nondirectional hypotheses, 165–167, 226–227
nondirectional tests, 243–244
nonparametrics, 15
normal distribution
Central Limit Theorem, 191–195
characteristics of, 169–170
kurtosis, 172–174
skewness, 170–172
confidence interval, 180–181
constructing, 182–189
Descriptive Statistics tool (Data Analysis add-in), 189–191
hypothesis testing, 191
NORM.DIST() function, 175
cumulative probability, requesting, 176
point estimate, requesting, 177
NORM.INV() function, 177–179
NORM.S.DIST() function, 179–180
NORM.S.INV() function, 180
unit normal distribution, 174–175
NORM.DIST() function, 175, 205, 208
cumulative probability, requesting, 176
point estimate, requesting, 177
NORM.INV() function, 177–179
NORM.S.DIST() function, 179–180
NORM.S.INV() function, 180
rejecting, 218–219
numeric scales, 14–15
O
observational research
multiple regression, 345–348
unequal group sizes, managing, 356–359
observations, pairing, 237
omnibus test, 277
one-tailed hypotheses, 226
one-way pivot tables, 113
creating, 114–116
statistical test, running, 116–120
ordinal scales, 14
orthogonal coding, 312
P
pairing observations, 237
parameters, 71
noncentrality parameters, 306
partial correlation, 327
partitioning
scores, 261–262
sum of squares between groups, 263, 266–268
sum of squares within groups, 263–265
variance, 230
pivot tables
frequency distributions, building, 28–31
Index display, 147–148
mode, calculating, 50–52
one-way, 113
creating, 114–116
statistical test, running, 116–120
two-way, 129–132
independence of classifications, testing, 133–139
independent events, 132–133
probabilities, 132–133
planned contrasts, multiple comparisons, 394–395
planned orthogonal contrasts, 283–286
platykurtic curve, 172
point estimate, 208
pooled variance, 229
positive correlation, 79
positively skewed frequency distributions, 21–22
probabilities, 132–133
problems with Excel’s documentation, 149–151
proportional cell frequencies, 302
proportions of variance, 312–315
purposes of ANCOVA
bias reduction, 362–363
greater power, 362
R
random factors, 306
random selection, making assumptions, 120–122
randomized blocks, 303
range, measuring variability, 62–64
ratio scales, 15
regression, 82, 95–96, 98, 101–104
residuals, 330–332
variance estimates, 316–317
regression slopes, ANCOVA, 370–372
rejecting null hypotheses, 218–219
relative addressing (Excel), extending semipartials, 332–335
removing bias, ANCOVA, 375–379
repeated measures design, 303
research hypotheses, 198–199
residual error, 362
residuals, 330–332
returning the result, 39–40
S
samples, tallying, 25
Sampling Techniques (1977), 152
category scales, 12–14
numeric scales, 14–15
Scatter charts. See XY charts
Scheffe method of multiple comparisons, 278–283, 389–393
scores, partitioning, 261–262
sum of squares between groups, 263, 266–268
sum of squares within groups, 263–265
semipartial correlation, 326–327
extending with absolute/relative addressing (Excel), 332–335
sum of squares, achieving with squared semipartial, 327–328
TREND() function, 328–330
setting the alpha level, 204
setting up worksheets for Solver, 44–46
shared variance, 105–106, 108–110
Simpson’s paradox, 140
simulated frequency distributions, building, 31–32
Single Factor ANOVA tool (Excel), 322–323
skewed distributions, 47
skewness as characteristic of normal distribution, 170–172
SLOPE() function, 102–104
Solver (Excel), 42–43
installing, 43
worksheets, setting up, 44–46
solving unbalanced factorial designs with multiple regression, 337–338
correlation matrices, 339–340
fluctuating proportions of variance, 344–345
order of entry, 340–344
standard deviation, 64–68
degrees of freedom, 74–75
functions, 75–76
variance, calculating, 69, 72–73
standard error
calculating for dependent groups, 247–251
underestimating, 238
standard error of the mean, 183, 200–204, 230
error rates, 204–205
statistical control, exerting with semipartial correlations, 326–327
statistical power, 219–220
alpha, 220–223
beta, 220
of directional tests, 244
increasing with ANCOVA, 363
versus ANOVA, 363–365
covariate, adding to analysis, 365–372
influences on, 257
STDEV() function, 75
STDEVA() function, 76
STDEVP() function, 75
STDEV.P() function, 76
STDEVPA() function, 76
STDEV.S() function, 76
studentized range statistic, 277
sum of squares,
achieving with squared semipartial, 327–328
within groups, 263–265
Survey Sampling (1995), 152
symbols used in formulas, 71–72
syntax, T.TEST() function, 239–240
Tails argument, 240–245
Type argument, 245–251
T
tables, 10
Tails argument (T.TEST() function), 240–245
tallying a sample, 25
T.DIST() function, 234–235
T.DIST.2T() function, 235
t-distribution, 214
T.DIST.RT() function, 235
testing
critical value, finding, 217–218
F tests, 268–270
hypotheses, 225
directional hypotheses, 226–234
nondirectional hypotheses, 228
means, 198
charts, creating, 206–212
standard error of the mean, 202–205
statistical power, 219–220
t-test, 213–216
z-test, 199–201
text values, distinguishing from interval values, 15–17
threats to internal validity
chance, 155–156
history, 153–154
instrumentation, 154
maturation, 154
mortality, 155
regression, 154
selection, 153
testing, 154
T.INV() function, 217, 232–234
total cross-product, 387
TREND() function, 99–101, 328–330
multiple regression, 104–106
residuals, 330–332
trend lines, 18–19
T-TEST() function, 236–238
T.TEST() function, 239
arrays, identifying, 239–240
Tails argument, 240–245
Type argument, 245
independent observations, 245–247
standard error, calculating for dependent groups, 247–251
T-Test Paired Two Sample for Means (Data Analysis add-in), 237
T-Test: Two-Sample Assuming Unequal Variances (Data Analysis add-in), 239
t-tests
capitalizing on chance, 260
degrees of freedom, 236
dependent group t-tests, performing, 249–256
directional hypotheses, making, 230
means, testing, 213–214
decision rule, defining, 215–216
observations, pairing, 237
reasons for not using, 259–261
unequal group variances, 237–238
when to avoid, 258
two-tailed hypotheses, 226
two-tailed tests, 243
two-test groups, degrees of freedom, 236
two-way pivot tables, 129–132
independence of classifications, testing, 133–135
CHISQ.DIST() function, 137–139
CHISQ.INV() function, 137–139
chi-square distributions, 135–137
independent events, 132–133
probabilities, 132–133
Type argument (T.TEST() function), 245
independent observations, 245–247
standard error, calculating for dependent groups, 247–251
U
unbalanced factorial designs, 302
solving with multiple regression, 337–338
correlation matrices, 339–340
fluctuating proportions of variance, 344–345
order of entry, 340–344
unbiased estimators, 74
underestimating standard error, 238
unequal group sizes, 275–277
in factorial ANOVA, 300–303
managing
in observational research, 356–359
in true experiments, 355–356
variances, 237–238
Unequal Variances t-Test tool (Data Analysis add-in), 255–256
unit normal distribution, 174–175
V
values
alpha, 186
counting with array formula, 53–55
interval values, distinguishing from text values, 15–17
VARA() function, 76
variability, measuring
with mean deviation, 70–71
with range, 62–64
variables, 9
charting, XY charts, 17–19
correlation, 79–81
calculating, 81–86
correlation coefficient, 80
multiple regression, 104–108
TREND() function, 99–101
values, 9
variance
ANOVA, 261
alpha, calculating, 270–271
design cells, 291–292
factorial ANOVA, 287–291
interaction, 293–300
scores, partitioning, 261–264
unequal group sizes, 275–277
estimates
via ANOVA, 315–316
via regression, 316–317
functions, 76
as parameter, 71–72
partitioning, 230
pooled variance, 229
shared variance, 105–106, 108–110
unequal group, 237
unequal group variances, 238
variance error of the mean, 201
VARP() function, 76
VAR.P() function, 77
VARPA() function, 77
VAR.S() function, 77
verifying directional hypotheses with t-test, 228–234
W
when to avoid t-tests, 258
within group variance, calculating, 264–265
worksheets, setting up for Solver, 44–46
X-Y-Z
XY charts, 17–19
Yule Simpson effect, 139–141
z-scores, 198
z-tests
critical value, finding, 216–217
means, testing, 199–201