class: center, middle, inverse, title-slide # How to t test ### Peter Higgins --- ### We will start with the tidy version from the {infer} package: t_test() #### Notice that you have to state the order of the two levels of your grouping variable --- class: split-40 count: false Tidy version from the {infer} package .left-code-ttest1-auto[ ```r *mtcars ``` ] .right-output-ttest1-auto[ ``` mpg cyl disp hp drat wt qsec vs Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 am gear carb Mazda RX4 1 4 4 Mazda RX4 Wag 1 4 4 Datsun 710 1 4 1 Hornet 4 Drive 0 3 1 Hornet Sportabout 0 3 2 Valiant 0 3 1 Duster 360 0 3 4 Merc 240D 0 4 2 Merc 230 0 4 2 Merc 280 0 4 4 Merc 280C 0 4 4 Merc 450SE 0 3 3 Merc 450SL 0 3 3 Merc 450SLC 0 3 3 Cadillac Fleetwood 0 3 4 Lincoln Continental 0 3 4 Chrysler Imperial 0 3 4 Fiat 128 1 4 1 Honda Civic 1 4 2 Toyota Corolla 1 4 1 Toyota Corona 0 3 1 Dodge Challenger 0 3 2 AMC Javelin 0 3 2 Camaro Z28 0 3 4 Pontiac Firebird 0 3 2 Fiat X1-9 1 4 1 Porsche 914-2 1 5 2 Lotus Europa 1 5 2 Ford Pantera L 1 5 4 Ferrari Dino 1 5 6 Maserati Bora 1 5 8 Volvo 142E 1 4 2 ``` ] --- class: split-40 count: false Tidy version from the {infer} package .left-code-ttest1-auto[ ```r mtcars %>% * select(mpg, cyl, am) ``` ] .right-output-ttest1-auto[ ``` mpg cyl am Mazda RX4 21.0 6 1 Mazda RX4 Wag 21.0 6 1 Datsun 710 22.8 4 1 Hornet 4 Drive 21.4 6 0 Hornet Sportabout 18.7 8 0 Valiant 18.1 6 0 Duster 360 14.3 8 0 Merc 240D 24.4 4 0 Merc 230 22.8 4 0 Merc 280 19.2 6 0 Merc 280C 17.8 6 0 Merc 450SE 16.4 8 0 Merc 450SL 17.3 8 0 Merc 450SLC 15.2 8 0 Cadillac Fleetwood 10.4 8 0 Lincoln Continental 10.4 8 0 Chrysler Imperial 14.7 8 0 Fiat 128 32.4 4 1 Honda Civic 30.4 4 1 Toyota Corolla 33.9 4 1 Toyota Corona 21.5 4 0 Dodge Challenger 15.5 8 0 AMC Javelin 15.2 8 0 Camaro Z28 13.3 8 0 Pontiac Firebird 19.2 8 0 Fiat X1-9 27.3 4 1 Porsche 914-2 26.0 4 1 Lotus Europa 30.4 4 1 Ford Pantera L 15.8 8 1 Ferrari Dino 19.7 6 1 Maserati Bora 15.0 8 1 Volvo 142E 21.4 4 1 ``` ] --- class: split-40 count: false Tidy version from the {infer} package .left-code-ttest1-auto[ ```r mtcars %>% select(mpg, cyl, am) %>% * filter(cyl > 5) ``` ] .right-output-ttest1-auto[ ``` mpg cyl am Mazda RX4 21.0 6 1 Mazda RX4 Wag 21.0 6 1 Hornet 4 Drive 21.4 6 0 Hornet Sportabout 18.7 8 0 Valiant 18.1 6 0 Duster 360 14.3 8 0 Merc 280 19.2 6 0 Merc 280C 17.8 6 0 Merc 450SE 16.4 8 0 Merc 450SL 17.3 8 0 Merc 450SLC 15.2 8 0 Cadillac Fleetwood 10.4 8 0 Lincoln Continental 10.4 8 0 Chrysler Imperial 14.7 8 0 Dodge Challenger 15.5 8 0 AMC Javelin 15.2 8 0 Camaro Z28 13.3 8 0 Pontiac Firebird 19.2 8 0 Ford Pantera L 15.8 8 1 Ferrari Dino 19.7 6 1 Maserati Bora 15.0 8 1 ``` ] --- class: split-40 count: false Tidy version from the {infer} package .left-code-ttest1-auto[ ```r mtcars %>% select(mpg, cyl, am) %>% filter(cyl > 5) %>% * t_test(mpg ~ am, * order = c("0", "1")) ``` ] .right-output-ttest1-auto[ ``` # A tibble: 1 x 6 statistic t_df p_value alternative lower_ci upper_ci <dbl> <dbl> <dbl> <chr> <dbl> <dbl> 1 -1.61 7.10 0.150 two.sided -5.98 1.12 ``` ] --- class: split-40 count: false Tidy version from the {infer} package .left-code-ttest1-auto[ ```r mtcars %>% select(mpg, cyl, am) %>% filter(cyl > 5) %>% t_test(mpg ~ am, order = c("0", "1")) # Interpreting the results # The t statistic is first # followed by degrees of freedom # then the p value # the default alternative: two.sided # then the confidence bounds # output is a tibble so that it is # easy to use these results ``` ] .right-output-ttest1-auto[ ``` # A tibble: 1 x 6 statistic t_df p_value alternative lower_ci upper_ci <dbl> <dbl> <dbl> <chr> <dbl> <dbl> 1 -1.61 7.10 0.150 two.sided -5.98 1.12 ``` ] <style> .left-code-ttest1-auto { color: #777; width: 38%; height: 92%; float: left; font-size: 80% } .right-output-ttest1-auto { width: 60%; float: right; padding-left: 1%; } </style> --- ### Now we will use the baseR version: t.test() #### Notice that you have to use `data = .` #### It is not quite as pipe-friendly --- class: split-40 count: false Base R Version .left-code-ttest2-auto[ ```r *mtcars ``` ] .right-output-ttest2-auto[ ``` mpg cyl disp hp drat wt qsec vs Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 am gear carb Mazda RX4 1 4 4 Mazda RX4 Wag 1 4 4 Datsun 710 1 4 1 Hornet 4 Drive 0 3 1 Hornet Sportabout 0 3 2 Valiant 0 3 1 Duster 360 0 3 4 Merc 240D 0 4 2 Merc 230 0 4 2 Merc 280 0 4 4 Merc 280C 0 4 4 Merc 450SE 0 3 3 Merc 450SL 0 3 3 Merc 450SLC 0 3 3 Cadillac Fleetwood 0 3 4 Lincoln Continental 0 3 4 Chrysler Imperial 0 3 4 Fiat 128 1 4 1 Honda Civic 1 4 2 Toyota Corolla 1 4 1 Toyota Corona 0 3 1 Dodge Challenger 0 3 2 AMC Javelin 0 3 2 Camaro Z28 0 3 4 Pontiac Firebird 0 3 2 Fiat X1-9 1 4 1 Porsche 914-2 1 5 2 Lotus Europa 1 5 2 Ford Pantera L 1 5 4 Ferrari Dino 1 5 6 Maserati Bora 1 5 8 Volvo 142E 1 4 2 ``` ] --- class: split-40 count: false Base R Version .left-code-ttest2-auto[ ```r mtcars %>% * select(mpg, cyl, am) ``` ] .right-output-ttest2-auto[ ``` mpg cyl am Mazda RX4 21.0 6 1 Mazda RX4 Wag 21.0 6 1 Datsun 710 22.8 4 1 Hornet 4 Drive 21.4 6 0 Hornet Sportabout 18.7 8 0 Valiant 18.1 6 0 Duster 360 14.3 8 0 Merc 240D 24.4 4 0 Merc 230 22.8 4 0 Merc 280 19.2 6 0 Merc 280C 17.8 6 0 Merc 450SE 16.4 8 0 Merc 450SL 17.3 8 0 Merc 450SLC 15.2 8 0 Cadillac Fleetwood 10.4 8 0 Lincoln Continental 10.4 8 0 Chrysler Imperial 14.7 8 0 Fiat 128 32.4 4 1 Honda Civic 30.4 4 1 Toyota Corolla 33.9 4 1 Toyota Corona 21.5 4 0 Dodge Challenger 15.5 8 0 AMC Javelin 15.2 8 0 Camaro Z28 13.3 8 0 Pontiac Firebird 19.2 8 0 Fiat X1-9 27.3 4 1 Porsche 914-2 26.0 4 1 Lotus Europa 30.4 4 1 Ford Pantera L 15.8 8 1 Ferrari Dino 19.7 6 1 Maserati Bora 15.0 8 1 Volvo 142E 21.4 4 1 ``` ] --- class: split-40 count: false Base R Version .left-code-ttest2-auto[ ```r mtcars %>% select(mpg, cyl, am) %>% * filter(cyl > 5) ``` ] .right-output-ttest2-auto[ ``` mpg cyl am Mazda RX4 21.0 6 1 Mazda RX4 Wag 21.0 6 1 Hornet 4 Drive 21.4 6 0 Hornet Sportabout 18.7 8 0 Valiant 18.1 6 0 Duster 360 14.3 8 0 Merc 280 19.2 6 0 Merc 280C 17.8 6 0 Merc 450SE 16.4 8 0 Merc 450SL 17.3 8 0 Merc 450SLC 15.2 8 0 Cadillac Fleetwood 10.4 8 0 Lincoln Continental 10.4 8 0 Chrysler Imperial 14.7 8 0 Dodge Challenger 15.5 8 0 AMC Javelin 15.2 8 0 Camaro Z28 13.3 8 0 Pontiac Firebird 19.2 8 0 Ford Pantera L 15.8 8 1 Ferrari Dino 19.7 6 1 Maserati Bora 15.0 8 1 ``` ] --- class: split-40 count: false Base R Version .left-code-ttest2-auto[ ```r mtcars %>% select(mpg, cyl, am) %>% filter(cyl > 5) %>% * t.test(mpg ~ am, data = .) ``` ] .right-output-ttest2-auto[ ``` Welch Two Sample t-test data: mpg by am t = -1.6145, df = 7.1019, p-value = 0.1498 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -5.981737 1.119237 sample estimates: mean in group 0 mean in group 1 16.06875 18.50000 ``` ] --- class: split-40 count: false Base R Version .left-code-ttest2-auto[ ```r mtcars %>% select(mpg, cyl, am) %>% filter(cyl > 5) %>% t.test(mpg ~ am, data = .) # Interpreting the results # The t statistic is first # followed by degrees of freedom # then the p value # then the alternative hypothesis # then the confidence bounds # then the mean mpg for each group ``` ] .right-output-ttest2-auto[ ``` Welch Two Sample t-test data: mpg by am t = -1.6145, df = 7.1019, p-value = 0.1498 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -5.981737 1.119237 sample estimates: mean in group 0 mean in group 1 16.06875 18.50000 ``` ] <style> .left-code-ttest2-auto { color: #777; width: 38%; height: 92%; float: left; font-size: 80% } .right-output-ttest2-auto { width: 60%; float: right; padding-left: 1%; } </style> --- <style type="text/css"> .remark-code{line-height: 1.5; font-size: 80%} </style> ### Which version of the t test do you like better? Discuss.