Table 1.
Statistical analysis of behavioral studiesa
| Parameter | Comparison | Results |
|---|---|---|
| Open field (WT, N = 23; Shank3WT/G, N = 19; Shank3G/G, N = 19) | ||
| Time in center | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.01, p = 0.90; main effect of genotype: F(2,55) = 1.15, p = 0.32; sex × genotype interaction: F(2,55) = 0.30, p = 0.73 |
| Frequency in center | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.07, p = 0.78; main effect of genotype: F(2,55) = 1.11, p = 0.33; sex × genotype interaction: F(2,55) = 0.67, p = 0.51 |
| Time in periphery | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.34, p = 0.55; main effect of genotype: F(2,55) = 0.26, p = 0.76; sex × genotype interaction: F(2,55) = 1.41, p = 0.25 |
| Frequency in periphery | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.80, p = 0.37; main effect of genotype: F(2,55) = 1.43, p = 0.24; sex × genotype interaction: F(2,55) = 2.47, p = 0.09 |
| Time in center/time in periphery | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.06, p = 0.79; main effect of genotype: F(2,55) = 1.20, p = 0.30; sex × genotype interaction: F(2,55) = 0.65, p = 0.52 |
| Distance traveled | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.01, p = 0.89; main effect of genotype: F(2,55) = 2.56, p = 0.08; sex × genotype interaction: F(2,55) = 2.75, p = 0.07 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.96; WT versus Shank3G/G: p < 0.05; Shank3WT/G versus Shank3G/G: p = 0.06 | ||
| Velocity | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.004, p = 0.94; main effect of genotype: F(2,55) = 2.35, p = 0.10; sex × genotype interaction: F(2,55) = 2.90, p = 0.06 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.96; WT versus Shank3G/G: p < 0.05; Shank3WT/G versus Shank3G/G: p = 0.07 | ||
| Dark/light box (WT, N = 23; Shank3WT/G, N = 19, Shank3G/G, N = 19) | ||
| Total activity | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.15, p = 0.69; main effect of genotype: F(2,55) = 2.96, p = 0.059; sex × genotype interaction: F(2,55) = 1.48, p = 0.23 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.99; WT versus Shank3G/G: p < 0.05; Shank3WT/G versus Shank3G/G: p < 0.05 | ||
| Time in light side | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.06, p = 0.79; main effect of genotype: F(2,55) = 0.87, p = 0.42; sex × genotype interaction: F(2,55) = 1.36, p = 0.26 |
| Crosses | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.20, p = 0.65; main effect of genotype: F(2,55) = 0.66, p = 0.51; sex × genotype interaction: F(2,55) = 2.12, p = 0.12 |
| Latency to enter light side | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.92, p = 0.33; main effect of genotype: F(2,55) = 6.66, p < 0.01; sex × genotype interaction: F(2,55) = 0.69, p = 0.50 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.38; WT versus Shank3G/G: p < 0.05; Shank3WT/G versus Shank3G/G: p < 0.001 | ||
| Time in dark side | Sex, genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.06, p = 0.79; main effect of genotype: F(2,55) = 0.87, p = 0.42; sex × genotype interaction: F(2,55) = 1.36, p = 0.26 |
| Elevated plus maze (WT, N = 23; Shank3WT/G, N = 19; Shank3G/G, N = 19) | ||
| Distance traveled | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.03, p = 0.85; main effect of genotype: F(2,55) = 4.83, p < 0.05; sex × genotype interaction: F(2,55) = 1.79, p = 0.17 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.99; WT versus Shank3G/G: p < 0.01; Shank3WT/G versus Shank3G/G: p < 0.01 | ||
| Velocity | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.03, p = 0.85; main effect of genotype: F(2,55) = 4.83, p < 0.05; sex × genotype interaction: F(2,55) = 1.79, p = 0.17 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.99; WT versus Shank3G/G: p < 0.01; Shank3WT/G versus Shank3G/G: p < 0.01 | ||
| Time in open arms/time in both arms | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.17, p = 0.68; main effect of genotype: F(2,55) = 0.23, p = 0.79; sex × genotype interaction: F(2,55) = 0.24, p = 0.78 |
| Entries in open/entries in both | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 3.52, p = 0.06; main effect of genotype: F(2,55) = 0.24, p = 0.78; sex × genotype interaction: F(2,55) = 0.62, p = 0.54 |
| Morris water maze: initial training (WT, N = 22; Shank3WT/G, N = 19; Shank3G/G, N = 18) | ||
| Latency to reach platform | Sex, genotype, and day | 3-way rmANOVA; main effect of sex: F(1,53) = 0.94, p = 0.33; main effect of genotype: F(2,53) = 3.83, p < 0.05; main effect of day: F(8,424) = 38.03, p < 0.001; sex × genotype interaction: F(2,53) = 1.07, p = 0.34; sex × day interaction: F(8,424) = 0.43, p = 0.90; genotype × day interaction: F(16,424) = 0.76, p = 0.73; sex × genotype × day interaction: F(16,424) = 0.80, p = 0.67 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.30; WT versus Shank3G/G: p < 0.05; Shank3WT/G versus Shank3G/G: p = 0.49 | ||
| Distance traveled to platform | Sex, genotype, and day | 3-way rmANOVA; main effect of sex: F(1,53) = 1.22, p = 0.27; main effect of genotype: F(2,53) = 5.61, p < 0.01; main effect of day: F(8,424) = 144.53, p < 0.001; sex × genotype interaction: F(2,53) = 0.71, p = 0.49; sex × day interaction: F(8,424) = 0.49, p = 0.86; genotype × day interaction: F(16,424) = 5.58, p < 0.001; sex × genotype × day interaction: F(16,424) = 0.90, p = 0.56 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.88; WT versus Shank3G/G: p < 0.01; Shank3WT/G versus Shank3G/G: p < 0.05 | ||
| Thigmotaxis | Sex, genotype, and day | 3-way rmANOVA; main effect of sex: F(1,53) = 0.20, p = 0.65; main effect of genotype: F(2,53) = 0.99, p = 0.37; main effect of day: F(8,424) = 44.17, p < 0.001; sex × genotype interaction: F(2,53) = 0.52, p = 0.59; sex × day interaction: F(8,424) = 0.21, p = 0.98; genotype × day interaction: F(16,424) = 1.48, p = 0.10; sex × genotype × day interaction: F(16,424) = 0.69, p = 0.79 |
| Average swim speed | Sex, genotype, and day | 3-way rmANOVA; main effect of sex: F(1,53) = 0.78, p = 0.37; main effect of genotype: F(2,53) = 36.66, p < 0.001; main effect of day: F(8,424) = 34.05, p < 0.001; sex × genotype interaction: F(2,53) = 0.44, p = 0.64; sex × day interaction: F(8,424) = 0.64, p = 0.74; genotype × day interaction: F(16,424) = 9.79, p < 0.001; sex × genotype × day interaction: F(16,424) = 0.54, p = 0.92 |
| Tukey HSD: WT versus Shank3WT/G: p < 0.001; WT versus Shank3G/G: p < 0.001 Shank3WT/G versus Shank3G/G: p < 0.05 | ||
| Morris water maze: probe trial (WT, N = 22; Shank3WT/G, N = 19; Shank3G/G, N = 18) | ||
| % time in quadrant | Sex, genotype, and quadrant | 3-way rmANOVA; main effect of sex: F(1,53) = 0.00000001, p = 0.99; main effect of genotype: F(2,53) = 0.00000008, p = 0.99; main effect of quadrant: F(3,159) = 20.621, p < 0.001; sex × genotype interaction: F(2,53) = 0.0000002, p = 0.99; sex × quadrant interaction: F(3,159) = 1.91, p = 0.13; genotype × quadrant interaction: F(6,159) = 0.89, p = 0.50; sex × genotype × quadrant interaction: F(6,159) = 1.20, p = 0.30 |
| Target versus other quadrants | Tukey HSD: target NW versus right NE: p < 0.001; target NW versus left SW: p < 0.001; target NW versus opposite SE: p < 0.001 | |
| Target versus other quadrants within WT | Tukey HSD: target NW versus right NE: p = 0.78 target NW versus left SW: p = 0.40; target NW versus opposite SE: p < 0.05 | |
| Target versus other quadrants within Shank3WT/G | Tukey HSD: target NW versus right NE: p < 0.001; target NW versus left SW: p < 0.001; target NW versus opposite SE: p < 0.001 | |
| Target versus other quadrants within Shank3G/G | Tukey HSD: target NW versus right NE: p < 0.01; target NW versus left SW: p < 0.05; target NW versus opposite SE: p < 0.001 | |
| No. of platform crossings | Sex, genotype, and platform | 3-way rmANOVA; main effect of sex: F(1,53) = 2.54, p = 0.11; main effect of genotype: F(2,53) = 1.56, p = 0.21; main effect of quadrant: F(3,159) = 25.05, p < 0.001; sex × genotype interaction: F(2,53) = 0.35, p = 0.70; sex × quadrant interaction: F(3,159) = 2.50, p = 0.06; genotype × quadrant interaction: F(6,159) = 1.36, p = 0.23; sex × genotype × quadrant interaction: F(6,159) = 0.72, p = 0.62 |
| Target versus other platforms | Tukey HSD: target NW versus right NE: p < 0.001; target NW versus left SW: p < 0.001; target NW versus opposite SE: p < 0.001 | |
| Target versus other platforms within WT | Tukey HSD: target NW versus right NE: p = 0.06 target NW versus left SW: p = 0.37; target NW versus opposite SE: p < 0.01 | |
| Target versus other platforms within Shank3WT/G | Tukey HSD: target NW versus right NE: p < 0.001; target NW versus left SW: p < 0.001; target NW versus opposite SE: p < 0.001 | |
| Target versus other platforms within Shank3G/G | Tukey HSD: target NW versus right NE: p < 0.01; target NW versus left SW: p < 0.05; target NW versus opposite SE: p < 0.001 | |
| Average swim speed | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,53) = 0.03, p = 0.85; main effect of genotype: F(2,53) = 1.45, p = 0.24; sex × genotype interaction: F(2,53) = 0.14, p = 0.86 |
| % thigmotaxis | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,53) = 0.21, p = 0.64; main effect of genotype: F(2,53) = 0.07, p = 0.93; sex × genotype interaction: F(2,53) = 1.11, p = 0.33 |
| Distance traveled | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,53) = 0.02, p = 0.86; main effect of genotype: F(2,53) = 1.49, p = 0.23; sex × genotype interaction: F(2,53) = 0.13, p = 0.87 |
| Visible water maze (WT, N = 22; Shank3WT/G, N = 19; Shank3G/G, N = 18) | ||
| Latency to platform | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,53) = 0.30, p = 0.58; main effect of genotype: F(2,53) = 2.87, p = 0.06; sex × genotype interaction: F(2,53) = 0.71, p = 0.49 |
| % thigmotaxis | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,32) = 0.0008, p = 0.97; main effect of genotype: F(1,32) = 0.98, p = 0.32; sex × genotype: F(1,32) = 0.04, p = 0.82 |
| Distance traveled to platform | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,53) = 0.02, p = 0.88; main effect of genotype: F(2,53) = 9.32, p < 0.001; sex × genotype interaction: F(2,53) = 0.81, p = 0.44 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.70; WT versus Shank3G/G: p < 0.01; Shank3WT/G versus Shank3G/G: p < 0.001 | ||
| Average swim speed | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,53) = 0.12, p = 0.72; main effect of genotype: F(2,53) = 5.12, p < 0.01; sex × genotype interaction: F(2,53) = 0.66, p = 0.51 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.10; WT versus Shank3G/G: p < 0.01; Shank3WT/G versus Shank3G/G: p = 0.52 | ||
| Nesting behavior (WT, N = 23; Shank3WT/G, N = 19; Shank3G/G, N = 19) | ||
| Increase in nest height | Sex, genotype, and time | 3-way rmANOVA; main effect of sex: F(1,55) = 0.114, p = 0.73; main effect of genotype: F(2,55) = 7.19, p < 0.01; main effect of time: F(2,110) = 21.03, p < 0.001; sex × genotype interaction: F(2,55) = 2.18, p = 0.12; sex × time interaction: F(2,110) = 0.39, p = 0.67; genotype × time interaction: F(4,110) = 1.07, p = 0.37; sex × genotype × time interaction: F(4,110) = 0.85, p = 0.49 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.37; WT versus Shank3G/G: p < 0.01; Shank3WT/G versus Shank3G/G: p = 0.24 | ||
| Increase in nest width | Sex, genotype, and time | 3-way rmANOVA; main effect of sex: F(1,55) = 0.71, p = 0.40; main effect of genotype: F(2,55) = 4.60, p < 0.05; main effect of time: F(2,110) = 23.64, p < 0.001; sex × genotype interaction: F(2,55) = 1.62, p = 0.20; sex × time interaction: F(2,110) = 1.73, p = 0.18; genotype × time interaction: F(4,110) = 0.71, p = 0.58; sex × genotype × time interaction: F(4,110) = 0.18, p = 0.94 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.77; WT versus Shank3G/G: p < 0.05; Shank3WT/G versus Shank3G/G: p = 0.10 | ||
| Three choice interaction test: baseline (WT, N = 19; Shank3WT/G, N = 15; Shank3G/G, N = 15) | ||
| Distance traveled | Sex and genotype | 2-way ANOVA: main effect of sex: F(1,43) = 0.34, p = 0.55; main effect of genotype: F(2,43) = 6.85, p < 0.01; sex × genotype interaction: F(2,43) = 0.24, p = 0.78 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.99; WT versus Shank3G/G: p < 0.01; Shank3WT/G versus Shank3G/G: p < 0.01 | ||
| Velocity | Sex and genotype | 2-way ANOVA: main effect of sex: F(1,43) = 0.0007, p = 0.97; main effect of genotype: F(2,43) = 6.44, p < 0.01; sex × genotype interaction: F(2,43) = 0.26, p = 0.76 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.99; WT versus Shank3G/G: p < 0.01; Shank3WT/G versus Shank3G/G: p < 0.05 | ||
| Time spent sniffing | Sex, genotype, and interaction target (front vs back) | 3-way rmANOVA: main effect of sex: F(1,43) = 0.0001, p = 0.99; main effect of genotype: F(2,43) = 1.37, p = 0.26; main effect of target: F(1,43) = 1.28, p = 0.26; sex × genotype interaction: F(2,43) = 0.004, p = 0.99; sex × target interaction: F(1,43) = 0.14, p = 0.70; genotype × target interaction: F(2,43) = 0.50, p = 0.60; sex × genotype × target interaction: F(2,43) = 0.16, p = 0.84 |
| Three choice interaction test: social preference (WT, N = 19; Shank3WT/G, N = 15; Shank3G/G, N = 15) | ||
| Distance traveled | Sex and genotype | 2-way ANOVA: main effect of sex: F(1,43) = 4.59, p < 0.05; main effect of genotype: F(2,43) = 1.85; p = 0.16; sex × genotype interaction: F(2,43) = 1.25, p = 0.29 |
| Velocity | Sex and genotype | 2-way ANOVA: main effect of sex: F(1,43) = 3.30, p = 0.07; main effect of genotype: F(2,43) = 1.60; p = 0.21; sex × genotype interaction: F(2,43) = 1.46, p = 0.24 |
| Time spent sniffing | Sex, genotype, and interaction target (inanimate vs social) | 3-way rmANOVA: main effect of sex: F(1,43) = 0.001, p = 0.96; main effect of genotype: F(2,43) = 0.144, p = 0.86; main effect of target: F(1,43) = 6.01, p < 0.05; sex × genotype interaction: F(2,43) = 0.46, p = 0.62; sex × target interaction: F(1,43) = 0.06, p = 0.79; genotype × target interaction: F(2,43) = 0.02, p = 0.97; sex × genotype × target interaction: F(2,43) = 2.25, p = 0.11 |
| Effect of target (inanimate vs social) within each genotype | Tukey HSD: WT: p = 0.60; Shank3WT/G: p = 0.77; Shank3G/G: p = 0.80 | |
| Three choice interaction test: social novelty (WT, N = 19; Shank3WT/G, N = 15; Shank3G/G, N = 15) | ||
| Distance traveled | Sex and genotype | 2-way ANOVA: main effect of sex: F(1,43) = 4.59, p < 0.05; main effect of genotype: F(2,43) = 1.85; p = 0.16; sex × genotype interaction: F(2,43) = 1.25, p = 0.29 |
| Velocity | Sex and genotype | 2-way ANOVA: main effect of sex: F(1,43) = 3.30, p = 0.07; main effect of genotype: F(2,43) = 1.60; p = 0.21; sex × genotype interaction: F(2,43) = 1.46, p = 0.24 |
| Time spent sniffing | Genotype and interaction target (familiar vs stranger) | 3-way rmANOVA: main effect of sex: F(1,43) = 0.257, p = 0.61; main effect of genotype: F(2,43) = 0.07, p = 0.93; main effect of target: F(1,43) = 4.52, p < 0.05; sex × genotype interaction: F(2,43) = 0.26, p = 0.76; sex × target interaction: F(1,43) = 1.88, p = 0.17; genotype × target interaction: F(2,43) = 31, p = 0.73; sex × genotype × target interaction: F(2,43) = 0.06, p = 0.93 |
| Effect of target (familiar vs novel) within each genotype | Tukey HSD: WT: p = 0.91; Shank3WT/G: p = 0.48; Shank3G/G: p = 0.92 | |
| Locomotor habituation (WT, N = 23; Shank3WT/G, N = 19; Shank3G/G, N = 19) | ||
| Total beam breaks | Sex, genotype, and bin | 3-way rmANOVA; main effect of sex: F(1,55) = 0.20, p = 0.65; main effect of genotype: F(2,55) = 0.38, p = 0.68; main effect of trial: F(23,1265) = 105.79, p < 0.001; sex × genotype interaction: F(2,55) = 2.62, p = 0.08; sex × trial interaction: F(23,1265) = 0.94, p = 0.53; genotype × trial: F(46,1265) = 1.72, p < 0.01; sex × genotype × trial interaction: F(46,1265) = 1.21, p = 0.16 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.97; WT versus Shank3G/G: p = 0.49; Shank3WT/G versus Shank3G/G: p = 0.40 | ||
| First bin only | Genotype and sex | 2-way ANOVA; main effect of sex: F(1,55) = 0.38, p = 0.53; main effect of genotype: F(2,55) = 10.85, p < 0.001; sex × genotype interaction: F(2,55) = 0.50, p = 0.60 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.96; WT versus Shank3G/G: p < 0.001; Shank3WT/G versus Shank3G/G: p < 0.001 | ||
| Stereotypy beam breaks | Sex, genotype, and bin | 3-way rmANOVA; main effect of sex: F(1,55) = 5.95, p < 0.05; main effect of genotype: F(2,55) = 1.18, p = 0.31; main effect of trial: F(23,1265) = 50.59, p < 0.001; sex × genotype interaction: F(2,55) = 3.78, p < 0.05; sex × trial interaction: F(23,1265) = 0.70, p = 0.84; genotype × trial: F(46,1265) = 0.84, p = 0.76; sex × genotype × trial interaction: F(46,1265) = 1.30, p = 0.08 |
| Ambulatory beam breaks | Sex, genotype, and bin | 3-way rmANOVA; main effect of sex: F(1,55) = 0.03, p = 0.84; main effect of genotype: F(2,55) = 1.21, p = 0.30; main effect of trial: F(23,1265) = 101.88, p < 0.001; sex × genotype interaction: F(2,55) = 2.03, p = 0.14; sex × trial interaction: F(23,1265) = 1.03, p = 0.41; genotype × trial: F(46,1265) = 2.16, p < 0.001; sex × genotype × trial interaction: F(46,1265) = 0.99, p = 0.47 |
| Rotarod (WT, N = 23; Shank3WT/G, N = 19; Shank3G/G, N = 19) | ||
| Time to fall off | Sex, genotype, and trial | 3-way rmANOVA; main effect of sex: F(1,55) = 12.36, p < 0.001; main effect of genotype: F(2,55) = 20.37, p < 0.001; main effect of trial: F(7,385) = 23.36, p < 0.001; sex × genotype interaction: F(2,55) = 3.73, p < 0.05; sex × trial interaction: F(7,238) = 0.51, p = 0.82; genotype × trial: F(14,385) = 1.25, p = 0.27; sex × genotype × trial interaction: F(14,385) = 0.60, p = 0.86 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.10; WT versus Shank3G/G: p < 0.001; Shank3WT/G versus Shank3G/G: p < 0.01 | ||
| Marble burying (WT, N = 23; Shank3WT/G, N = 19; Shank3G/G, N = 19) | ||
| No. of marbles buried | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 1.31, p = 0.25; main effect of genotype: F(2,55) = 9.80, p < 0.001; sex × genotype interaction: F(2,55) = 0.29, p = 0.74 |
| Tukey HSD: WT versus Shank3WT/G: p = 0.10; WT versus Shank3G/G: p < 0.001; Shank3WT/G versus Shank3G/G: p = 0.06 | ||
| Grooming (WT, N = 23; Shank3WT/G, N = 19; Shank3G/G, N = 19) | ||
| Time spent grooming | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.53, p = 0.46; main effect of genotype: F(2,55) = 0.97, p = 0.38; sex × genotype interaction: F(2,55) = 1.27, p = 0.28 |
| No. of bouts | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.004, p = 0.94; main effect of genotype: F(2,55) = 0.73, p = 0.48; sex × genotype interaction: F(2,55) = 0.09, p = 0.91 |
| Time per bout | Sex and genotype | 2-way ANOVA; main effect of sex: F(1,55) = 0.12, p = 0.72; main effect of genotype: F(2,55) = 0.69, p = 0.50; sex × genotype interaction: F(2,55) = 1.25, p = 0.29 |
a WT, Wild-type; rmANOVA, ANOVA (between-subjects factors are generally sex and genotype) with repeated measures (day, time, or trial); F(x, y), F ratio statistic used to determine whether the variances in two independent samples are equal; x, y, degrees of freedom (df), a measure of the number of independent pieces of information on which the precision of a parameter estimate is based. × = number of groups − 1; y = number of animals per group − 1, multiplied by the number of groups.