_ X SE_ (z)
AP Biology – Statistics
5.99
Calculating Error Bars for a Graph Mean – the average of the numbers in a data set Standard Error – statistical accuracy of a single data set, which is an estimation of standard deviation Standard Deviation –range in which typical values fall above or below the mean in a large sample or population. Error Bar Parameters – range above and below the mean in which the actual data value could fall.
Formula on AP Reference Table – but just take the average of the numbers in the data set. Formula on AP Reference Table Formula on AP Reference Table
_ X
+ -
SE_ (z) X
SEM
Figure 1. Bacterial Biofilm Thickness over Time
Given or from z-value Table (depends on df)
Title the Graph – relationship between two variables. Independent Variable on x-Axis – Title (units) Dependent Variable on y-Axis – Title (units) Even Scale on Both Axes – start with zero – avoid breaks Plot the Mean with Error Bars Draw Trendline (line of best fit) through error bars – do not connect to zero unless it is a data point Label Data Sets with a Key Slope = Rate Slope = ΔY/ΔX (Take Points from Line of Best Fit) 1
Error Bars In your lab activities use t for your z value
2
Chi-Square Test – use with counted data • • •
Number of cells with and without a specific characteristic. Number of offspring with and without a specific characteristic. Number of animals or plants preferring one condition over another condition.
Null Hypothesis – Statement of No Difference There is no statistically significant difference between the (experimental group) and (control group). Calculate Chi-square Value
Formula on AP Reference Table
Have one factor for each category of outcome. Tall and Short (2 factors) Tall, Medium, Short (3 factors) Determine Degrees of Freedom
Instructions on AP Reference Table
Find Critical Chi-Square Value on Table Find Critical P-Value on Table
Table on AP Reference Table
Fail to Accept Null Hypothesis (Reject Null Hypothesis) – A Statistically Significant Difference Does Exist. • •
Chi-Square Value is greater than the Critical Chi-Square Value on Table P-Value determined on Table is less than 0.05
Fail to Reject Null Hypothesis (Accept Null Hypothesis) – A Statistically Significant Difference Does NOT Exist. • •
Chi-Square Value is less than the Critical Chi-Square Value P-Value determined on Table is greater than 0.05
Drug or Environmental Factor Testing – if the goal is to show that a drug or factor has an influence, failing to accept (rejecting) the null hypothesis will statistically support that the drug or factor has an influence.
Goal – Fail to Accept Null Hypothesis
Genetics Problems – if the goal is to show that results from a Mendelian genetics cross are close enough to ideal predicted percentages, accepting the null hypothesis is the desired option and will show that results are close enough to be considered valid.
Goal – Fail to Reject the Null Hypothesis
3
t-Test – use with measured data that is averaged • • • • •
Oxygen consumption (mL) during respiration Carbon dioxide production (mL) during respiration Change in mass (g) due to diffusion Water loss (mL) due to transpiration Color change in guaiacol (%T) due to peroxidase activity
Null Hypothesis – Statement of No Difference There is no statistically significant difference between the (experimental group) and (control group). There is no statistically significant difference between (experimental condition 1) and (experimental condition 2). Calculate t –Value
Ti-84 calculator or t-value must be given in problem
Determine Degrees of Freedom Find Critical t-Value on Table Find Critical P-Value on Table
Ti-84 calculator or use instructions on AP Reference Table
Must be given – not on AP Reference Table
Fail to Accept Null Hypothesis (Reject Null Hypothesis) – A Statistically Significant Difference Does Exist. • t-Value is greater than the Critical t-Value • P-Value is less than 0.05 Fail to Reject Null Hypothesis (Accept Null Hypothesis) – A Statistically Significant Difference Does NOT Exist • t-Value is less than the t-Value • P-Value is greater than 0.05 * Statistically Different from Control + Statistically Different from another Experimental Condition
Control
Experimental 1 Experimental 2 Figure 2.The Effect of Homocysteine Concentration on MTT Reduction.
4
5.99
Calculating Error Bars for a Graph Mean – the average of the numbers in a data set Standard Error – statistical accuracy of a single data set, which is an estimation of standard deviation Standard Deviation –range in which typical values fall above or below the mean in a large sample or population. Error Bar Parameters – range above and below the mean in which the actual data value could fall.
Formula on AP Reference Table – but just take the average of the numbers in the data set. Formula on AP Reference Table Formula on AP Reference Table
_ X
+ -
SE_ (z) X
SEM
Figure 1. Bacterial Biofilm Thickness over Time
Given or from z-value Table (depends on df)
Title the Graph – relationship between two variables. Independent Variable on x-Axis – Title (units) Dependent Variable on y-Axis – Title (units) Even Scale on Both Axes – start with zero – avoid breaks Plot the Mean with Error Bars Draw Trendline (line of best fit) through error bars – do not connect to zero unless it is a data point Label Data Sets with a Key Slope = Rate Slope = ΔY/ΔX (Take Points from Line of Best Fit) 1
Error Bars In your lab activities use t for your z value
2
Chi-Square Test – use with counted data • • •
Number of cells with and without a specific characteristic. Number of offspring with and without a specific characteristic. Number of animals or plants preferring one condition over another condition.
Null Hypothesis – Statement of No Difference There is no statistically significant difference between the (experimental group) and (control group). Calculate Chi-square Value
Formula on AP Reference Table
Have one factor for each category of outcome. Tall and Short (2 factors) Tall, Medium, Short (3 factors) Determine Degrees of Freedom
Instructions on AP Reference Table
Find Critical Chi-Square Value on Table Find Critical P-Value on Table
Table on AP Reference Table
Fail to Accept Null Hypothesis (Reject Null Hypothesis) – A Statistically Significant Difference Does Exist. • •
Chi-Square Value is greater than the Critical Chi-Square Value on Table P-Value determined on Table is less than 0.05
Fail to Reject Null Hypothesis (Accept Null Hypothesis) – A Statistically Significant Difference Does NOT Exist. • •
Chi-Square Value is less than the Critical Chi-Square Value P-Value determined on Table is greater than 0.05
Drug or Environmental Factor Testing – if the goal is to show that a drug or factor has an influence, failing to accept (rejecting) the null hypothesis will statistically support that the drug or factor has an influence.
Goal – Fail to Accept Null Hypothesis
Genetics Problems – if the goal is to show that results from a Mendelian genetics cross are close enough to ideal predicted percentages, accepting the null hypothesis is the desired option and will show that results are close enough to be considered valid.
Goal – Fail to Reject the Null Hypothesis
3
t-Test – use with measured data that is averaged • • • • •
Oxygen consumption (mL) during respiration Carbon dioxide production (mL) during respiration Change in mass (g) due to diffusion Water loss (mL) due to transpiration Color change in guaiacol (%T) due to peroxidase activity
Null Hypothesis – Statement of No Difference There is no statistically significant difference between the (experimental group) and (control group). There is no statistically significant difference between (experimental condition 1) and (experimental condition 2). Calculate t –Value
Ti-84 calculator or t-value must be given in problem
Determine Degrees of Freedom Find Critical t-Value on Table Find Critical P-Value on Table
Ti-84 calculator or use instructions on AP Reference Table
Must be given – not on AP Reference Table
Fail to Accept Null Hypothesis (Reject Null Hypothesis) – A Statistically Significant Difference Does Exist. • t-Value is greater than the Critical t-Value • P-Value is less than 0.05 Fail to Reject Null Hypothesis (Accept Null Hypothesis) – A Statistically Significant Difference Does NOT Exist • t-Value is less than the t-Value • P-Value is greater than 0.05 * Statistically Different from Control + Statistically Different from another Experimental Condition
Control
Experimental 1 Experimental 2 Figure 2.The Effect of Homocysteine Concentration on MTT Reduction.
4
