Validity and Threats to Validity

Validity

Threats to Validity

Variability

  • Variability is a fundamental issue in research, concerning the amount of difference observable among people, situations, or things. It is more than standard deviation.

  • Variability is almost always present; the key considerations are:

    • The source of the variability.

    • How the variability is accounted for.

  • Unsystematic Variability: Essentially random variance, which is generally considered undesirable ("BAD").

    • Sources include individual differences within the sample/population and measurement error.

  • Systematic Variability: Variance that is accounted for among groups.

    • Caused by the independent variable (IV) or treatment manipulation.

  • Extraneous Variance: Undesirable variance resulting from differences among groups for reasons outside of the controlled intervention; this is also known as a confounding variable.

Threats to Validity

Internal Validity

  • Internal validity refers to whether observed changes among people or differences in the population are due to the designed intervention or variables of interest.

    • Strong internal validity implies that the observed changes are indeed due to the intervention.

  • A threat to internal validity exists if changes observed in the study (or differences observed among groups) are due to factors outside the planned investigation.

    • These threats arise when an irrelevant variable "messes up" the study findings, indicating poor control.

External Validity

  • External validity concerns whether the findings of the study are generalizable to the population of interest.

    • Population Validity: Indicates whether the findings apply to people outside of the study.

    • Ecological Validity: Indicates whether the findings can be applied to conditions outside of the study.

Threats to Internal Validity: DIFFERENCES BETWEEN GROUPS

  • Maturation: Changes occur due to the typical development of the sample.

  • Selection: Bias or error in the selection of subjects accounts for the findings.

  • Selection X Maturation: The effect of maturation differs based on selection.

  • Statistical Regression (Regression to the Mean): When selecting extreme groups, anticipate that they will naturally regress towards the mean.

  • Mortality: Withdrawal or loss of participants skews the results.

  • Instrumentation: Measurement issues underlie the outcomes.

  • Testing: Involvement with dependent variable (DV) measures influences outcomes (e.g., the testing effect).

  • History: Something happened during the study that accounts for the findings.

  • Resentful Demoralization of Control Group: The control group becomes demoralized and performs worse due to feeling left out.

Threats to Internal Validity: SIMILARITIES AMONG GROUPS

  • Diffusion of Treatment: "Seepage effect," where the treatment affects the control group.

  • Compensatory Rivalry: "John Henry effect," where the control group works harder to compete with the treatment group.

  • Compensatory Equalization of Treatment: "Clinician's dilemma," where efforts are made to equalize treatment between groups, compromising the integrity of the intervention.

Threats to External Validity: POPULATION VALIDITY

  • Generalization Across Subjects (Participants): There are limits to the ability to expect that the study's outcome will be applicable to the general population (sampling frame).

  • Interaction of "Personological" Variables and Treatment Effects: An unaccounted-for within-sample factor in the experimental group causes a differential outcome, affecting the ability to generalize to the population at large.

Threats to External Validity

  • Verification of IV: Also known as Treatment Fidelity.

  • Multiple Treatment Interference: The effects of multiple treatments overlap (e.g., common in reading research).

  • Hawthorne Effect: Participants alter their behavior because they know they are being observed.

  • Novelty & Disruption Effects: Similar to the Hawthorne effect, where newness or disruption influences outcomes.

  • Experimenter Effects: Common in treatment interventions delivered by an expert (the creator of the intervention).

  • Pretest Sensitization: Critical when only the experimental group has the pretest, influencing their reactions to the treatment.

  • Posttest Sensitization: Only an issue when the posttest itself accounts for the outcome of the findings.

  • History X Treatment: Something else happened during the study that affected the treatment outcome.

  • Measurement of DV: "Straw Man," where the measurement of the dependent variable does not accurately reflect the intended construct.

  • Interaction of Time of Measurement & Treatment Effect: The intervention is only effective within a limited parameter of the assessment period in the study.

Other Validity Concerns

Statistical Validity

  • Studies using statistics meet the expectation of statistical validity when predetermined levels of "confidence" are met.

  • Attention to the appropriate use of statistics is crucial (avoid "fishing" for results).

Social Validity

  • The study provides use to the society involved.

  • Goals of study are socially relevant.

  • Study outputs were worth the “cost”.

  • Findings demonstrate a meaningful outcome for society (statistical significance does not mean practical significance).

Validity
Threats to Validity
Variability
  • Variability is a fundamental issue in research, concerning the amount of difference observable among people, situations, or things. It is more than standard deviation.

  • Variability is almost always present; the key considerations are:

    • The source of the variability.

    • How the variability is accounted for.

  • Unsystematic Variability: Essentially random variance, which is generally considered undesirable ("BAD").

    • Sources include individual differences within the sample/population and measurement error.

  • Systematic Variability: Variance that is accounted for among groups.

    • Caused by the independent variable (IV) or treatment manipulation.

  • Extraneous Variance: Undesirable variance resulting from differences among groups for reasons outside of the controlled intervention; this is also known as a confounding variable.

Threats to Validity
Internal Validity
  • Internal validity refers to whether observed changes among people or differences in the population are due to the designed intervention or variables of interest.

    • Strong internal validity implies that the observed changes are indeed due to the intervention.

  • A threat to internal validity exists if changes observed in the study (or differences observed among groups) are due to factors outside the planned investigation.

    • These threats arise when an irrelevant variable "messes up" the study findings, indicating poor control.

External Validity
  • External validity concerns whether the findings of the study are generalizable to the population of interest.

    • Population Validity: Indicates whether the findings apply to people outside of the study.

    • Ecological Validity: Indicates whether the findings can be applied to conditions outside of the study.

Threats to Internal Validity: DIFFERENCES BETWEEN GROUPS
  • Maturation: Changes occur due to the typical development of the sample.

  • Selection: Bias or error in the selection of subjects accounts for the findings.

  • Selection X Maturation: The effect of maturation differs based on selection.

  • Statistical Regression (Regression to the Mean): When selecting extreme groups, anticipate that they will naturally regress towards the mean.

  • Mortality: Withdrawal or loss of participants skews the results.

  • Instrumentation: Measurement issues underlie the outcomes.

  • Testing: Involvement with dependent variable (DV) measures influences outcomes (e.g., the testing effect).

  • History: Something happened during the study that accounts for the findings.

  • Resentful Demoralization of Control Group: The control group becomes demoralized and performs worse due to feeling left out.

Threats to Internal Validity: SIMILARITIES AMONG GROUPS
  • Diffusion of Treatment: "Seepage effect," where the treatment affects the control group.

  • Compensatory Rivalry: "John Henry effect," where the control group works harder to compete with the treatment group.

  • Compensatory Equalization of Treatment: "Clinician's dilemma," where efforts are made to equalize treatment between groups, compromising the integrity of the intervention.

Threats to External Validity: POPULATION VALIDITY
  • Generalization Across Subjects (Participants): There are limits to the ability to expect that the study's outcome will be applicable to the general population (sampling frame).

  • Interaction of "Personological" Variables and Treatment Effects: An unaccounted-for within-sample factor in the experimental group causes a differential outcome, affecting the ability to generalize to the population at large.

Threats to External Validity
  • Verification of IV: Also known as Treatment Fidelity.

  • Multiple Treatment Interference: The effects of multiple treatments overlap (e.g., common in reading research).

  • Hawthorne Effect: Participants alter their behavior because they know they are being observed.

  • Novelty & Disruption Effects: Similar to the Hawthorne effect, where newness or disruption influences outcomes.

  • Experimenter Effects: Common in treatment interventions delivered by an expert (the creator of the intervention).

  • Pretest Sensitization: Critical when only the experimental group has the pretest, influencing their reactions to the treatment.

  • Posttest Sensitization: Only an issue when the posttest itself accounts for the outcome of the findings.

  • History X Treatment: Something else happened during the study that affected the treatment outcome.

  • Measurement of DV: "Straw Man," where the measurement of the dependent variable does not accurately reflect the intended construct.

  • Interaction of Time of Measurement & Treatment Effect: The intervention is only effective within a limited parameter of the assessment period in the study.

Other Validity Concerns
Statistical Validity
  • Studies using statistics meet the expectation of statistical validity when predetermined levels of "confidence" are met.

  • Attention to the appropriate use of statistics is crucial (avoid "fishing" for results).

Social Validity
  • The study provides use to the society involved.

  • Goals of study are socially relevant.

  • Study outputs were worth the “cost”.

  • Findings demonstrate a meaningful outcome for society (statistical significance does not mean practical significance).

Validity
Threats to Validity
Variability
  • Variability is a fundamental issue in research, concerning the amount of difference observable among people, situations, or things. It is more than standard deviation.

  • Variability is almost always present; the key considerations are:

    • The source of the variability.

    • How the variability is accounted for.

  • Unsystematic Variability: Essentially random variance, which is generally considered undesirable ("BAD").

    • Sources include individual differences within the sample/population and measurement error.

  • Systematic Variability: Variance that is accounted for among groups.

    • Caused by the independent variable (IV) or treatment manipulation.

  • Extraneous Variance: Undesirable variance resulting from differences among groups for reasons outside of the controlled intervention; this is also known as a confounding variable.

Threats to Validity
Internal Validity
  • Internal validity refers to whether observed changes among people or differences in the population are due to the designed intervention or variables of interest.

    • Strong internal validity implies that the observed changes are indeed due to the intervention.

  • A threat to internal validity exists if changes observed in the study (or differences observed among groups) are due to factors outside the planned investigation.

    • These threats arise when an irrelevant variable "messes up" the study findings, indicating poor control.

External Validity
  • External validity concerns whether the findings of the study are generalizable to the population of interest.

    • Population Validity: Indicates whether the findings apply to people outside of the study.

    • Ecological Validity: Indicates whether the findings can be applied to conditions outside of the study.

Threats to Internal Validity: DIFFERENCES BETWEEN GROUPS
  • Maturation: Changes occur due to the typical development of the sample.

  • Selection: Bias or error in the selection of subjects accounts for the findings.

  • Selection X Maturation: The effect of maturation differs based on selection.

  • Statistical Regression (Regression to the Mean): When selecting extreme groups, anticipate that they will naturally regress towards the mean.

  • Mortality: Withdrawal or loss of participants skews the results.

  • Instrumentation: Measurement issues underlie the outcomes.

  • Testing: Involvement with dependent variable (DV) measures influences outcomes (e.g., the testing effect).

  • History: Something happened during the study that accounts for the findings.

  • Resentful Demoralization of Control Group: The control group becomes demoralized and performs worse due to feeling left out.

Threats to Internal Validity: SIMILARITIES AMONG GROUPS
  • Diffusion of Treatment: "Seepage effect," where the treatment affects the control group.

  • Compensatory Rivalry: "John Henry effect," where the control group works harder to compete with the treatment group.

  • Compensatory Equalization of Treatment: "Clinician's dilemma," where efforts are made to equalize treatment between groups, compromising the integrity of the intervention.

Threats to External Validity: POPULATION VALIDITY
  • Generalization Across Subjects (Participants): There are limits to the ability to expect that the study's outcome will be applicable to the general population (sampling frame).

  • Interaction of "Personological" Variables and Treatment Effects: An unaccounted-for within-sample factor in the experimental group causes a differential outcome, affecting the ability to generalize to the population at large.

Threats to External Validity
  • Verification of IV: Also known as Treatment Fidelity.

  • Multiple Treatment Interference: The effects of multiple treatments overlap (e.g., common in reading research).

  • Hawthorne Effect: Participants alter their behavior because they know they are being observed.

  • Novelty & Disruption Effects: Similar to the Hawthorne effect, where newness or disruption influences outcomes.

  • Experimenter Effects: Common in treatment interventions delivered by an expert (the creator of the intervention).

  • Pretest Sensitization: Critical when only the experimental group has the pretest, influencing their reactions to the treatment.

  • Posttest Sensitization: Only an issue when the posttest itself accounts for the outcome of the findings.

  • History X Treatment: Something else happened during the study that affected the treatment outcome.

  • Measurement of DV: "Straw Man," where the measurement of the dependent variable does not accurately reflect the intended construct.

  • Interaction of Time of Measurement & Treatment Effect: The intervention is only effective within a limited parameter of the assessment period in the study.

Other Validity Concerns
Statistical Validity
  • Studies using statistics meet the expectation of statistical validity when predetermined levels of "confidence" are met.

  • Attention to the appropriate use of statistics is crucial (avoid "fishing" for results).

Social Validity
  • The study provides use to the society involved.

  • Goals of study are socially relevant.

  • Study outputs were worth the “cost”.

  • Findings demonstrate a meaningful outcome for society (statistical significance does not mean practical significance).

Validity
Threats to Validity
Variability
  • Variability is a fundamental issue in research, concerning the amount of difference observable among people, situations, or things. It is more than standard deviation.

  • Variability is almost always present; the key considerations are:

    • The source of the variability.

    • How the variability is accounted for.

  • Unsystematic Variability: Essentially random variance, which is generally considered undesirable ("BAD").

    • Sources include individual differences within the sample/population and measurement error.

  • Systematic Variability: Variance that is accounted for among groups.

    • Caused by the independent variable (IV) or treatment manipulation.

  • Extraneous Variance: Undesirable variance resulting from differences among groups for reasons outside of the controlled intervention; this is also known as a confounding variable.

Threats to Validity
Internal Validity
  • Internal validity refers to whether observed changes among people or differences in the population are due to the designed intervention or variables of interest.

    • Strong internal validity implies that the observed changes are indeed due to the intervention.

  • A threat to internal validity exists if changes observed in the study (or differences observed among groups) are due to factors outside the planned investigation.

    • These threats arise when an irrelevant variable "messes up" the study findings, indicating poor control.

External Validity
  • External validity concerns whether the findings of the study are generalizable to the population of interest.

    • Population Validity: Indicates whether the findings apply to people outside of the study.

    • Ecological Validity: Indicates whether the findings can be applied to conditions outside of the study.

Threats to Internal Validity: DIFFERENCES BETWEEN GROUPS
  • Maturation: Changes occur due to the typical development of the sample.

  • Selection: Bias or error in the selection of subjects accounts for the findings.

  • Selection X Maturation: The effect of maturation differs based on selection.

  • Statistical Regression (Regression to the Mean): When selecting extreme groups, anticipate that they will naturally regress towards the mean.

  • Mortality: Withdrawal or loss of participants skews the results.

  • Instrumentation: Measurement issues underlie the outcomes.

  • Testing: Involvement with dependent variable (DV) measures influences outcomes (e.g., the testing effect).

  • History: Something happened during the study that accounts for the findings.

  • Resentful Demoralization of Control Group: The control group becomes demoralized and performs worse due to feeling left out.

Threats to Internal Validity: SIMILARITIES AMONG GROUPS
  • Diffusion of Treatment: "Seepage effect," where the treatment affects the control group.

  • Compensatory Rivalry: "John Henry effect," where the control group works harder to compete with the treatment group.

  • Compensatory Equalization of Treatment: "Clinician's dilemma," where efforts are made to equalize treatment between groups, compromising the integrity of the intervention.

Threats to External Validity: POPULATION VALIDITY
  • Generalization Across Subjects (Participants): There are limits to the ability to expect that the study's outcome will be applicable to the general population (sampling frame).

  • Interaction of "Personological" Variables and Treatment Effects: An unaccounted-for within-sample factor in the experimental group causes a differential outcome, affecting the ability to generalize to the population at large.

Threats to External Validity
  • Verification of IV: Also known as Treatment Fidelity.

  • Multiple Treatment Interference: The effects of multiple treatments overlap (e.g., common in reading research).

  • Hawthorne Effect: Participants alter their behavior because they know they are being observed.

  • Novelty & Disruption Effects: Similar to the Hawthorne effect, where newness or disruption influences outcomes.

  • Experimenter Effects: Common in treatment interventions delivered by an expert (the creator of the intervention).

  • Pretest Sensitization: Critical when only the experimental group has the pretest, influencing their reactions to the treatment.

  • Posttest Sensitization: Only an issue when the posttest itself accounts for the outcome of the findings.

  • History X Treatment: Something else happened during the study that affected the treatment outcome.

  • Measurement of DV: "Straw Man," where the measurement of the dependent variable does not accurately reflect the intended construct.

  • Interaction of Time of Measurement & Treatment Effect: The intervention is only effective within a limited parameter of the assessment period in the study.

Other Validity Concerns
Statistical Validity
  • Studies using statistics meet the expectation of statistical validity when predetermined levels of "confidence" are met.

  • Attention to the appropriate use of statistics is crucial (avoid "fishing" for results).

Social Validity
  • The study provides use to the society involved.

  • Goals of study are socially relevant.

  • Study outputs were worth the “cost”.

  • Findings demonstrate a meaningful outcome for society (statistical significance does not mean practical significance).

Validity
Threats to Validity
Variability
  • Variability is a fundamental issue in research, concerning the amount of difference observable among people, situations, or things. It is more than standard deviation.

  • Variability is almost always present; the key considerations are:

    • The source of the variability.

    • How the variability is accounted for.

  • Unsystematic Variability: Essentially random variance, which is generally considered undesirable ("BAD").

    • Sources include individual differences within the sample/population and measurement error.

  • Systematic Variability: Variance that is accounted for among groups.

    • Caused by the independent variable (IV) or treatment manipulation.

  • Extraneous Variance: Undesirable variance resulting from differences among groups for reasons outside of the controlled intervention; this is also known as a confounding variable.

Threats to Validity
Internal Validity
  • Internal validity refers to whether observed changes among people or differences in the population are due to the designed intervention or variables of interest.

    • Strong internal validity implies that the observed changes are indeed due to the intervention.

  • A threat to internal validity exists if changes observed in the study (or differences observed among groups) are due to factors outside the planned investigation.

    • These threats arise when an irrelevant variable "messes up" the study findings, indicating poor control.

External Validity
  • External validity concerns whether the findings of the study are generalizable to the population of interest.

    • Population Validity: Indicates whether the findings apply to people outside of the study.

    • Ecological Validity: Indicates whether the findings can be applied to conditions outside of the study.

Threats to Internal Validity: DIFFERENCES BETWEEN GROUPS
  • Maturation: Changes occur due to the typical development of the sample.

  • Selection: Bias or error in the selection of subjects accounts for the findings.

  • Selection X Maturation: The effect of maturation differs based on selection.

  • Statistical Regression (Regression to the Mean): When selecting extreme groups, anticipate that they will naturally regress towards the mean.

  • Mortality: Withdrawal or loss of participants skews the results.

  • Instrumentation: Measurement issues underlie the outcomes.

  • Testing: Involvement with dependent variable (DV) measures influences outcomes (e.g., the testing effect).

  • History: Something happened during the study that accounts for the findings.

  • Resentful Demoralization of Control Group: The control group becomes demoralized and performs worse due to feeling left out.

Threats to Internal Validity: SIMILARITIES AMONG GROUPS
  • Diffusion of Treatment: "Seepage effect," where the treatment affects the control group.

  • Compensatory Rivalry: "John Henry effect," where the control group works harder to compete with the treatment group.

  • Compensatory Equalization of Treatment: "Clinician's dilemma," where efforts are made to equalize treatment between groups, compromising the integrity of the intervention.

Threats to External Validity: POPULATION VALIDITY
  • Generalization Across Subjects (Participants): There are limits to the ability to expect that the study's outcome will be applicable to the general population (sampling frame).

  • Interaction of "Personological" Variables and Treatment Effects: An unaccounted-for within-sample factor in the experimental group causes a differential outcome, affecting the ability to generalize to the population at large.

Threats to External Validity
  • Verification of IV: Also known as Treatment Fidelity.

  • Multiple Treatment Interference: The effects of multiple treatments overlap (e.g., common in reading research).

  • Hawthorne Effect: Participants alter their behavior because they know they are being observed.

  • Novelty & Disruption Effects: Similar to the Hawthorne effect, where newness or disruption influences outcomes.

  • Experimenter Effects: Common in treatment interventions delivered by an expert (the creator of the intervention).

  • Pretest Sensitization: Critical when only the experimental group has the pretest, influencing their reactions to the treatment.

  • Posttest Sensitization: Only an issue when the posttest itself accounts for the outcome of the findings.

  • History X Treatment: Something else happened during the study that affected the treatment outcome.

  • Measurement of DV: "Straw Man," where the measurement of the dependent variable does not accurately reflect the intended construct.

  • Interaction of Time of Measurement & Treatment Effect: The intervention is only effective within a limited parameter of the assessment period in the study.

Other Validity Concerns
Statistical Validity
  • Studies using statistics meet the expectation of statistical validity when predetermined levels of "confidence" are met.

  • Attention to the appropriate use of statistics is crucial (avoid "fishing" for results).

Social Validity
  • The study provides use to the society involved.

  • Goals of study are socially relevant.

  • Study outputs were worth the “cost”.

  • Findings demonstrate a meaningful outcome for society (statistical significance does not mean practical significance).

Validity
Threats to Validity
Variability
  • Variability is a fundamental issue in research, concerning the amount of difference observable among people, situations, or things. It is more than standard deviation.

  • Variability is almost always present; the key considerations are:

    • The source of the variability.

    • How the variability is accounted for.

  • Unsystematic Variability: Essentially random variance, which is generally considered undesirable ("BAD").

    • Sources include individual differences within the sample/population and measurement error.

  • Systematic Variability: Variance that is accounted for among groups.

    • Caused by the independent variable (IV) or treatment manipulation.

  • Extraneous Variance: Undesirable variance resulting from differences among groups for reasons outside of the controlled intervention; this is also known as a confounding variable.

Threats to Validity
Internal Validity
  • Internal validity refers to whether observed changes among people or differences in the population are due to the designed intervention or variables of interest.

    • Strong internal validity implies that the observed changes are indeed due to the intervention.

  • A threat to internal validity exists if changes observed in the study (or differences observed among groups) are due to factors outside the planned investigation.

    • These threats arise when an irrelevant variable "messes up" the study findings, indicating poor control.

External Validity
  • External validity concerns whether the findings of the study are generalizable to the population of interest.

    • Population Validity: Indicates whether the findings apply to people outside of the study.

    • Ecological Validity: Indicates whether the findings can be applied to conditions outside of the study.

Threats to Internal Validity: DIFFERENCES BETWEEN GROUPS
  • Maturation: Changes occur due to the typical development of the sample.

  • Selection: Bias or error in the selection of subjects accounts for the findings.

  • Selection X Maturation: The effect of maturation differs based on selection.

  • Statistical Regression (Regression to the Mean): When selecting extreme groups, anticipate that they will naturally regress towards the mean.

  • Mortality: Withdrawal or loss of participants skews the results.

  • Instrumentation: Measurement issues underlie the outcomes.

  • Testing: Involvement with dependent variable (DV) measures influences outcomes (e.g., the testing effect).

  • History: Something happened during the study that accounts for the findings.

  • Resentful Demoralization of Control Group: The control group becomes demoralized and performs worse due to feeling left out.

Threats to Internal Validity: SIMILARITIES AMONG GROUPS
  • Diffusion of Treatment: "Seepage effect," where the treatment affects the control group.

  • Compensatory Rivalry: "John Henry effect," where the control group works harder to compete with the treatment group.

  • Compensatory Equalization of Treatment: "Clinician's dilemma," where efforts are made to equalize treatment between groups, compromising the integrity of the intervention.

Threats to External Validity: POPULATION VALIDITY
  • Generalization Across Subjects (Participants): There are limits to the ability to expect that the study's outcome will be applicable to the general population (sampling frame).

  • Interaction of "Personological" Variables and Treatment Effects: An unaccounted-for within-sample factor in the experimental group causes a differential outcome, affecting the ability to generalize to the population at large.

Threats to External Validity
  • Verification of IV: Also known as Treatment Fidelity.

  • Multiple Treatment Interference: The effects of multiple treatments overlap (e.g., common in reading research).

  • Hawthorne Effect: Participants alter their behavior because they know they are being observed.

  • Novelty & Disruption Effects: Similar to the Hawthorne effect, where newness or disruption influences outcomes.

  • Experimenter Effects: Common in treatment interventions delivered by an expert (the creator of the intervention).

  • Pretest Sensitization: Critical when only the experimental group has the pretest, influencing their reactions to the treatment.

  • Posttest Sensitization: Only an issue when the posttest itself accounts for the outcome of the findings.

  • History X Treatment: Something else happened during the study that affected the treatment outcome.

  • Measurement of DV: "Straw Man," where the measurement of the dependent variable does not accurately reflect the intended construct.

  • Interaction of Time of Measurement & Treatment Effect: The intervention is only effective within a limited parameter of the assessment period in the study.

Other Validity Concerns
Statistical Validity
  • Studies using statistics meet the expectation of statistical validity when predetermined levels of "confidence" are met.

  • Attention to the appropriate use of statistics is crucial (avoid "fishing" for results).

Social Validity
  • The study provides use to the society involved.

  • Goals of study are socially relevant.

  • Study outputs were worth the “cost”.

  • Findings demonstrate a meaningful outcome for society (statistical significance does not mean practical significance).