Summarizing and Interpreting Data: Role of Statistics in Research

Statistics

  • Descriptive Statistics: Measures that summarize, organize, and describe a set of data

    • Used to describe the data

    • Many types of these statistics

      • Frequency distributions

      • Summary measures

      • Graphical representations of the data

    • A way to visualize the data

    • The first step in any statistical analysis

  • Inferential Statistics: Statistical procedures used by researchers to test hypotheses about populations

    • Interpret what the data means (measuring relationships, comparing group differences)

    • A significant effect means that it is unlikely to have occurred in the sample by chance

Describing the Data: Frequency

  • Frequency is the number of participants in each category OR count of how many times a score is scored

  • Useful for nominal and ordinal data, but can also be used for interval/ratio data

  • Percentage is the proportion of a score within a sample

Central Tendency

  • Central tendency is the middle of the distribution on the x-axis, average value (represents typical score in a distribution)

    • Mode: Most frequently occurring score

      • Can be used with all scales of measurement

    • Median: Middle score in the distribution (half of the scores are above and half are below that value

      • Can be used with ordered (ordinal) and scale data (interval, ratio)

    • Mean: The calculated average of all the scores

      • Can be used with scale data (interval, ratio)

Variability

  • INdificate show much the scores in the distribution differ from each other across the response scale

    • The horizontal spread of the distribution, deviation from average value

  • Range: Highest value-lowest value

  • Standard deviation: average distance between the scores and the mean

    • Indicates how much individuals in your sample differ from the sample mean

  • Variance: Standard deviation squared

Hypothesis Testing

  • Null Hypothesis

    • Predicts no effect or relationship in the population

      • Prediction that is statistically tested

      • If p-value is less than .05 reject null hypothesis (significant different or relationship)

  • Scientific/Alternative Hypothesis

    • Predicts there is an effect or relationship in the population

      • Prediction about the results of the study

Inferential Statistics

  • Significance testing

    • The p value is less than or equal to alpha in an inferential test, and the null hypothesis can be rejected

    • Alpha level

      • The probability level used by researchers to indicate the cutoff probability level (highest value) that allows them to reject the null hypothesis

    • p Value

      • The probability value associated with inferential test

      • Indicates likelihood of obtaining the data in a study when the null hypothesis is true

Hypothesis Examples

  • Research Question: Do memory abilities change as people age

    • Scientific/Alternative Hypothesis: Memory abilities change with age

    • Null hypothesis: Memory abilities do not change with age

One-Tailed vs. Two-Tailed Hypothesis

  • One-Tailed

    • Happy dog will eat more?

      • Yes/No

  • Two-Tailed

    • Mood affects the appetite of dogs

      • Eat more/Eat less

One-Trailed Hypothesis Examples

  • Research Question: Do memory abilities change as people age?

    • Scientific/Alternative hypothesis: Older individuals have lower memory scores than younger individuals

    • Null hypothesis: The memory scores of the two age groups are the same OR older individuals have higher memory scores than younger individuals

Hypothesis Testing Terminology

  • There is no difference in the measured variable between the two groups studied

    • Statistics terms: Fail to reject H0

    • APA Terms: results do not support our hypothesis

  • There is a difference in the measured variable between the two groups studied

    • Statistics terms: reject H0

    • APA Terms: Results SUPPORT our hypothesis

Errors in Hypothesis Testing

  • Type I Error: Reject null when it’s true (false positive)

    • More serious than Type II errors

    • Probability of making a Type I error: a (alpha)

      • Generally set at .05: only a 5% chance of committing a Type I error

  • Type II Error: Fail to reject null when it is false (False negative)

    • Can be caused by low statistical power due to small sample size