Evaluating & Modeling Experiments - ACT Science

1. What does a high standard deviation indicate about a data set?

   Data points are spread out over a wide range. Values are far from the average, showing variability.

2. Which type of error is due to random fluctuations in measurements?

   Random error. Unpredictable variations that cannot be controlled.

3. What is the best interpretation of a best-fit line on a scatterplot?

   It approximates the overall trend relating the two variables. Shows the general relationship despite individual data scatter.

4. What is an experimental group?

   The group that receives the treatment or condition being tested. Allows comparison with control to measure treatment effects.

5. What should be measured: 'Effects of fertilizer on plant height'?

   Plant height. The outcome variable affected by fertilizer treatment.

6. Identify the confounding variable if light differs between groups in a plant-growth study.

   Light level. This uncontrolled factor could affect plant growth results.

7. What is the difference between correlation and causation?

   Correlation is association; causation requires a direct effect. Causation means one variable directly influences another.

8. What is a confounding variable?

   An external variable affecting both independent and dependent variables. Third variable that influences both measured variables.

9. What should be constant: Testing effect of light on plant growth?

   Soil type, water, and temperature. Controls for variables other than light intensity.

10. Define a confounding variable.

    An extraneous variable that affects the outcome of an experiment. Creates alternative explanations that invalidate results.

11. What is a constant in an experiment?

    A factor that does not change throughout the experiment. Remains unchanged to isolate variable effects.

12. Choose the independent variable: Time of day vs. Sleep quality.

    Time of day. The factor researchers control and manipulate.

13. What is the dependent variable in an experiment?

    The measured response that depends on the independent variable. This is what you measure to see the effect of changes.

14. What is the role of peer review in scientific research?

    To evaluate and validate research findings. Experts check research quality before publication.

15. What is the primary reason for conducting a pilot study?

    To test feasibility and refine methodology. Small trial run identifies problems before main study.

16. What is the dependent variable in an experiment?

    The variable that is measured or observed in response to changes. It's the effect that researchers measure for changes.

17. What is a repeated measures design?

    An experimental design where the same subjects are used in all conditions. Reduces individual differences as confounding variables.

18. Identify a method to reduce bias in an experiment.

    Use randomization to assign subjects to groups. Ensures equal chance of assignment to any group.

19. What does 'statistically significant' mean in experimental results?

    Results unlikely due to chance, suggesting a real effect. Low probability the results occurred by random chance.

20. What is the $y$-intercept in a linear model $y = mx + b$?

    $b$, the value of $y$ when $x = 0$. Shows where the line crosses the vertical axis.

21. What is replication in experimental design?

    Repeating trials or experiments to check consistency of results. Confirms results are reliable and not due to chance.

22. Use $y = 2x + 1$ to find $y$ when $x = 4$.

    $y = 9$. Substitute $x = 4$: $y = 2(4) + 1 = 9$

23. Identify the main goal of experimental modeling.

    To simulate and analyze real-world processes to make predictions. Creates testable representations of complex systems.

24. Identify the type of error that occurs when a measurement is consistently off by the same amount.

    Systematic error. Consistent bias in one direction affects all measurements.

25. Select the dependent variable: Fertilizer amount vs. Crop yield.

    Crop yield. The outcome measured in agricultural experiments.

26. Identify whether estimating $y$ at $x = 10$ is extrapolation if data span $x = 1$ to $5$.

    Extrapolation. Estimating beyond the observed data range is extrapolation.

27. Use $y = 5 - x$ to find $x$ when $y = 1$.

    $x = 4$. Substitute $y = 1$: $1 = 5 - x$, so $x = 4$

28. What does it mean if a graph shows a linear relationship between variables?

    The variables change at an approximately constant rate. Data points form a straight line pattern.

29. Identify the control group in an experiment testing a new drug's effectiveness.

    Group receiving placebo. This group receives no treatment for comparison.

30. What is a confounding variable?

    An uncontrolled factor that can affect the dependent variable. Can create misleading results by affecting the outcome.

31. Identify the dependent variable if temperature is set and reaction rate is measured.

    Reaction rate. This variable responds to changes in temperature.

32. What does a correlation coefficient of 0 indicate?

    No linear relationship between variables. Variables are completely independent of each other.

33. Correct the conclusion: 'Data supports hypothesis' with one trial.

    Conduct multiple trials to ensure reliability. Single trials cannot establish reliable patterns.

34. Identify the relationship if points cluster around a horizontal line as $x$ increases.

    No correlation (approximately constant $y$). Horizontal pattern shows $y$ doesn't change with $x$.

35. Find the error in this hypothesis: 'Plants grow faster in the dark.'

    Specify measurable variables like growth rate and light condition. Hypothesis lacks measurable, operational definitions.

36. Identify the relationship if points trend downward from left to right on a scatterplot.

    Negative correlation. Downward trend indicates negative relationship between variables.

37. Which variable is manipulated to test its effect on another variable?

    Independent variable. The researcher controls and changes this factor.

38. What is a double-blind experiment?

    Neither participants nor researchers know assigned groups. Prevents bias from expectations affecting results.

39. What does it mean if an experiment is repeatable?

    The results can be consistently replicated under the same conditions. Demonstrates reliability and validity of findings.

40. Which option is the correct conclusion if only the independent variable changes across trials?

    Differences in results can be attributed to the independent variable. Only the treatment varies, so it caused any differences.

41. What is the primary function of a hypothesis?

    To provide a basis for experimental testing. Creates testable predictions for experiments to verify.

42. What does a p-value indicate in hypothesis testing?

    Probability of observing results as extreme as the observed. Lower p-values suggest results are not due to chance.

43. Which group receives a placebo?

    Control group. Controls for psychological treatment effects.

44. Correct the experimental design: Results affected by confounding variables.

    Identify and control confounding variables. Eliminates alternative explanations for observed effects.

45. Identify the control group if plants get fertilizer A, fertilizer B, or no fertilizer.

    The no-fertilizer group. This group receives no treatment for comparison.

46. Which phase of the scientific method involves testing a hypothesis?

    Experimentation. Controlled tests determine if hypotheses are supported.

47. Identify the flaw: Results based on a small sample size.

    Increase the sample size for more reliable results. Larger samples reduce random error and increase validity.

48. What does it mean if an experiment is 'replicable'?

    It can be repeated with similar results. Other researchers get consistent results using same methods.

49. Identify the error: No randomization in group assignment.

    Use randomization to assign subjects to groups. Eliminates selection bias in experimental design.

50. What is the slope in a linear model $y = mx + b$?

    $m$, the change in $y$ per unit change in $x$. Shows how steep the line is and direction of change.

51. Identify the independent variable if temperature is set and reaction rate is measured.

    Temperature. The experimenter controls this variable to test its effect.

52. What is the purpose of a double-blind study?

    To prevent bias by keeping both subjects and experimenters unaware of group assignments. Eliminates expectation bias from all participants.

53. Define a control group in an experiment.

    A group that does not receive the experimental treatment. Provides baseline comparison to show treatment effects.

54. What is interpolation when using a graph or model?

    Estimating within the range of observed data. Predictions are more reliable within the data range.

55. What is a sample size?

    The number of observations or subjects in an experiment. Larger sizes increase reliability and statistical power.

56. Which method is used to ensure random assignment in an experiment?

    Randomization. Eliminates bias by randomly assigning subjects.

57. What is the dependent variable: Temperature vs. Reaction rate?

    Reaction rate. The outcome measured in response to temperature changes.

58. Identify one purpose of a control variable.

    To keep conditions constant to isolate the effect of the independent variable. Eliminates alternative explanations for results.

59. Identify the independent variable: Water temperature affects fish activity.

    Water temperature. The factor being deliberately manipulated by researchers.

60. Choose the correct claim if two variables correlate but no mechanism or control is shown.

    Correlation is shown; causation is not established. Correlation exists, but causation requires experimental evidence.

61. Which statistical measure indicates the spread of a data set?

    Standard deviation. Measures how far data points vary from the mean.

62. What is the primary goal of data analysis in experiments?

    To interpret and draw conclusions from data. Extract meaningful patterns and relationships from results.

63. What is the operational definition of a variable?

    The exact procedure used to measure or define the variable. Makes the measurement method clear and repeatable.

64. What is the purpose of a placebo in an experiment?

    To control for effects caused by expectation rather than treatment. Eliminates psychological effects from knowing treatment status.

65. What ensures experiment validity?

    Control of variables, randomization, and replication. Essential components for reliable scientific conclusions.

66. What is the purpose of a hypothesis in an experiment?

    To propose a testable explanation or prediction. It guides the experiment and can be tested.

67. Which option best describes a negative correlation between $x$ and $y$?

    As $x$ increases, $y$ decreases. Variables move in opposite directions from each other.

68. What is the median of the data set: 3, 8, 2, 5, 9?

    5. Middle value when ordered: 2, 3, 5, 8, 9.

69. Correct the experimental setup: Control group receives treatment.

    Control group should not receive any experimental treatment. Control groups must remain untreated for valid comparison.

70. Which variable is manipulated: Study on effect of sunlight on algae growth?

    Amount of sunlight. The controlled factor being tested for effects.

71. What is an outlier in a data set?

    A data point significantly different from others. Extreme value that doesn't fit the general pattern.

72. What does random assignment help reduce in an experiment?

    Systematic bias from preexisting group differences. Ensures groups are equivalent before treatment begins.

73. What term describes a factor that is kept constant to prevent influence on the outcome?

    Controlled variable. These factors must remain constant to ensure valid results.

74. What is the independent variable in an experiment?

    The variable that is manipulated or changed by the experimenter. It's the cause that researchers control to test effects.

75. What is a placebo?

    An inactive substance or treatment given to the control group. Controls for psychological effects of treatment expectation.

76. What is the purpose of a control variable?

    To isolate the effect of the independent variable. Prevents other factors from affecting the results.

77. What does an outlier represent in a data set?

    A data point far from the overall pattern or trend. May indicate measurement error or unusual conditions.

78. State the formula for calculating the mean of a data set.

    $\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$. Add all values and divide by the count.

79. Which graph type is most suitable for displaying trends over time?

    Line graph. Shows continuous data changes over time periods.

80. What is a hypothesis in the context of an experiment?

    A testable prediction about how the independent variable affects the dependent variable. States the expected relationship between variables.

81. What does it mean if results are statistically significant?

    The observed effect is unlikely due to random chance alone. The probability of getting this result by chance is very low.

82. What is the main objective of a control in an experiment?

    To provide a baseline for comparison. Shows what happens without experimental treatment.

83. What is extrapolation when using a graph or model?

    Estimating beyond the range of observed data. Predictions become less reliable outside the data range.

84. What is a hypothesis?

    A testable prediction about the relationship between variables. Must be specific and measurable to be scientifically valid.

85. Which type of graph is best for comparing categories?

    Bar graph. Best for discrete categories or groups.

86. What is the difference between systematic error and random error?

    Systematic shifts results consistently; random varies unpredictably. Systematic error is predictable; random error is not.

87. What is the difference between accuracy and precision?

    Accuracy is closeness to true value; precision is repeatability. Accuracy hits the target; precision groups shots together.

88. What is the purpose of a literature review in research?

    To survey existing research and identify gaps. Examines previous studies to build research foundation.

89. In a graph, what does the x-axis typically represent?

    The independent variable. Shows what researchers manipulate or change.

90. What is the role of a hypothesis in scientific research?

    To provide a basis for experimentation and prediction. Guides experimental design and data interpretation.

91. What is a controlled variable (constant) in an experiment?

    A factor kept the same across all trials. Ensures fair comparison by eliminating other influences.

92. Identify the error in this experiment: No control variables used.

    Introduce control variables to maintain constant conditions. Control variables prevent confounding of results.

93. What is the term for a testable statement or prediction in research?

    Hypothesis. Proposed explanation that can be experimentally tested.

94. Choose the dependent variable: Temperature vs. Solubility.

    Solubility. The measured response to temperature changes.

95. Which option best supports causation: randomized experiment or observational study?

    Randomized experiment. Random assignment allows causal conclusions to be drawn.

96. Find the flaw: Experiment without a hypothesis.

    Develop a testable hypothesis to guide the experiment. Hypotheses provide direction and focus for research.

97. Which term describes the variable that is changed in an experiment?

    Independent variable. The researcher deliberately alters this variable.

98. What is a control group in an experiment?

    A baseline group not receiving the experimental treatment. Provides comparison to isolate the treatment effect.

99. Find $b$ in $y = mx + b$ if $m = 3$ and the line passes through $(2, 11)$.

    $b = 5$. Substitute point into $y = mx + b$: $11 = 3(2) + b$, so $b = 5$.

100. Which type of bias occurs when the sample is not representative of the population?

     Sampling bias. Sample doesn't accurately reflect the target population.

101. What is the independent variable in an experiment measuring plant growth with different fertilizers?

     Type of fertilizer. This is what the researcher changes or manipulates.

102. Identify the independent variable: Sugar concentration vs. Fermentation rate.

     Sugar concentration. The factor deliberately varied to test effects.

103. In a graph, what does the y-axis typically represent?

     The dependent variable. Shows what researchers measure as the outcome.

104. What is the range of the data set: 4, 7, 1, 9, 3?

     8. Largest minus smallest value: 9 - 1 = 8.

105. What is a model in scientific data analysis?

     A simplified representation used to describe or predict a system. Helps explain patterns and make predictions from data.

106. What is the mode of the data set: 4, 4, 5, 7, 9?

     4. Most frequently occurring value in the data set.

107. Find the slope if $y$ increases from $2$ to $8$ when $x$ increases from $1$ to $4$.

     $m = 2$. Slope = $\frac{\text{rise}}{\text{run}} = \frac{8-2}{4-1} = 2$

108. Which type of study prevents placebo effects?

     Double-blind study. Prevents bias from both subjects and researchers.

109. What is the dependent variable in an experiment measuring the effect of sunlight on plant height?

     Plant height. This is what changes in response to sunlight.

110. Identify whether estimating $y$ at $x = 3$ is interpolation if data span $x = 1$ to $5$.

     Interpolation. Estimating within the observed data range is interpolation.

111. Identify the variable that is measured in an experiment.

     Dependent variable. This responds to changes in the independent variable.

112. Choose the correct term: Variable that responds to changes.

     Dependent variable. Responds to changes in independent variables.

113. Which option best describes a positive correlation between $x$ and $y$?

     As $x$ increases, $y$ increases. Both variables move in the same direction together.

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