Transcript Slide 1
Using and Understanding 95% Confidence Intervals in BIOL 1011 # of bubbles produced (your bench) mean # of bubbles produced (n= 6 ) 100 cm (light off) 100cm (light on) 50cm (light on) 25cm (light on) 12 cm (light on) 0 3 15 38 49 0.25 4.35 18.65 36.20 51.15 # of bubbles produced (your bench) mean # of bubbles produced (n= 6 ) 100 cm (light off) 100cm (light on) 50cm (light on) 25cm (light on) 12 cm (light on) 0 3 15 38 49 0.25 4.35 18.65 36.20 51.15 are they different? 100 cm (light off) 100cm (light on) 50cm (light on) 25cm (light on) 12 cm (light on) 0 3 15 38 49 0.25 4.35 18.65 36.20 51.15 # of bubbles produced (your bench) mean # of bubbles produced (n= 6 ) are they different? mean # of bubbles produced (n= 6 ) mean # of bubbles produced (n= 6 ) 100 cm (light off) 100cm (light on) 50cm (light on) 25cm (light on) 12 cm (light on) 0 6.75 20.00 41.65 62.85 100 cm (light off) 100cm (light on) 50cm (light on) 25cm (light on) 12 cm (light on) 1.1 2.25 14.85 22.45 38.35 100 cm (light off) 100cm (light on) 50cm (light on) 25cm (light on) 12 cm (light on) 0 3 15 38 49 0.25 4.35 18.65 36.20 51.15 # of bubbles produced (your bench) mean # of bubbles produced (n= 6 ) mean # of bubbles produced (n= 6 ) mean # of bubbles produced (n= 6 ) 100 cm (light off) 100cm (light on) 50cm (light on) 25cm (light on) 12 cm (light on) 0 6.75 20.00 41.65 62.85 100 cm (light off) 100cm (light on) 50cm (light on) 25cm (light on) 12 cm (light on) 1.1 2.25 14.85 22.45 38.35 sample means for Bacopa at 50 cm with 100W light sample means vary around the population mean 14.85 18.65 20.00 sample means vary around the population mean 14.85 18.65 20.00 standard error tells us how much a sample mean tends to vary from the population mean sample means vary around the population mean 14.85 18.65 20.00 standard error tells us how much a sample mean tends to vary from the population mean standard error = standard deviation / √ n sample means vary around the population mean 95% of sample means fall within 2 standard errors of the population mean 2SE 14.85 18.65 2SE 20.00 standard error tells us how much a sample mean tends to vary from the population mean standard error = standard deviation / √ n sample means vary around the population mean so, an interval of sample mean ± 2 standard errors is 95% likely to contain the population mean: it’s a 95% confidence interval 95% of sample means fall within 2 standard errors of the population mean 2SE 14.85 18.65 2SE 20.00 standard error tells us how much a sample mean tends to vary from the population mean standard error = standard deviation / √ n Using 95% confidence intervals to compare two means Calculate standard error (SE) for each mean using standard deviation and n Construct 95% confidence interval for each mean: sample mean ± 2SE Compare the two intervals: do they overlap? NO the means are likely to be significantly different YES the means are not likely to be significantly different Location Mean Age (years) Standard Deviation n West End 3.50 0.9 556 East End 3.60 0.7 442 Does mean age differ between west and east? Location Mean Age (years) Standard Deviation n West End 3.50 0.9 556 East End 3.60 0.7 442 Does mean age differ between west and east? Null hypothesis: There is no difference between mean age at west and east ends. Location Mean Age (years) Standard Deviation n West End 3.50 0.9 556 East End 3.60 0.7 442 Does mean age differ between west and east? Null hypothesis: There is no difference between mean age at west and east ends. 1. Find standard error for each. 2. Construct 95% confidence intervals for each. 3. Construct graph to visually compare confidence intervals. Do they overlap? Maternal Age at Birth of First Offspring 3.7 3.65 sample means 3.6 3.55 3.5 3.45 3.4 error bars (mean ± 2SE) 3.35 3.3 West End East End Location on Island 3. Construct graph to visually compare confidence intervals. Do they overlap? Maternal Age at Birth of First Offspring 3.7 3.65 3.6 3.55 3.5 3.45 3.4 3.35 3.3 West End East End Location on Island The intervals overlap, so we can say that the means are not likely to be different. We will not reject the null hypothesis that the means are not different.