Exam 1 Flashcards by Benjamin Kozak

Intro to Biostatistics

Statistical characteristic of population is a ?

Statistical characteristic of population is a parameter.

Population = The entire set of people in the group of interest

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Intro to Biostatistics

Statistical characteristic of sample is a ?

Statistical characteristic of sample is a statistic.

Sample = Subset of the population chosen for study.

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Intro to Biostatistics

The “spread” of the data = ?

Variability

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Intro to Biostatistics

Measures of Central Tendency?

Mean: average
Median: the score at which 50% of the scores are above and below
Divides scores in two equal halves
Mode: the score that occurs most frequently

Median is between mean and mode in skewed distributions.

Central Tendency = the statistical measure that identifies a single value as representative of an entire distribution.”

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Intro to Biostatistics

Shapes of distributions include?

Normal (B):

Skewed to right (A):
* The “tail” faces right; not where the bulk of the curve lies
* AKA “positive skew”
* Mean > median/mode

Skewed to left (C):
* The “tail” faces left
* AKA “negative skew”
* Mean < median/mode

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Intro to Biostatistics

The Normal Distribution

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Intro to Biostatistics

68% of the scores are within +/- _ ? _ SD of the mean.

The Normal Distribution

68% of the scores are within +/- 1 SD of the mean.

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Intro to Biostatistics

95% of the scores are within +/- _ ? _ SD of the mean.

The Normal Distribution

95% of the scores are within +/- 2 SD of the mean.

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Intro to Biostatistics

99% of the scores are within +/- _ ? _ SD of the mean.

The Normal Distribution

99% of the scores are within +/- 3 SD of the mean.

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Intro to Biostatistics

A z-score of “2” is interpreted as?

A z-score of “2” is interpreted as 2 standard deviations from the mean

Z-Score: A standardized score based on the normal distribution
z = standard deviation units

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Foundations of Statistical Inference

The likelihood that any one event will occur, given all the possible outcomes = ?

Probability = The likelihood that any one event will occur, given all the possible outcomes.

Represented by a lowercase p
Implies uncertainty – what is likely to happen
Essential to understand inferential statistics
Many statistical tests assume data are normally distributed
Relationship to normal distribution

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Foundations of Statistical Inference

Sampling error measured by ?

Sampling error measured by the standard error of the mean.

The sample mean won’t equal the population mean = Difference is called sampling error.
If you repeat the study using new samples from the SAME population, how much with the sample mean vary?

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Foundations of Statistical Inference

A range of values that we are confident contains the population parameter = ?

Confidence Interval = A range of values that we are confident contains the population parameter.
Width concerns the precision of the estimate

95% Confidence Interval =
* If we repeated sampling an infinite number of times, 95% of the intervals would overlap the true mean

The 95% CI of 5 from 100 samples will not overlap the true population mean

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Foundations of Statistical Inference

Reject Ho + Ho is true = __?__

Potential Errors in Hypothesis Testing

Type 1 error / Liar

False positive / Dr. says “You’re pregnant” + you’re male

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Foundations of Statistical Inference

Reject Ho + Ho is false = ?

Potential Errors in Hypothesis Testing

Correct

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Foundations of Statistical Inference

Accept “do not reject “ Ho + Ho is true = ?

Potential Errors in Hypothesis Testing

Correct

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Foundations of Statistical Inference

Accept “do not reject “ Ho + Ho is False = __?__

Potential Errors in Hypothesis Testing

Type 2 Error / Blind

False negative, You’re pregnant + Dr. says “You’re not pregnant”

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Foundations of Statistical Inference

Alpha = ?

Maximum probability of type 1 error
Set by researcher before running statistics
Usually set to 0.05 (max chance of type 1 error = 5%)

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Foundations of Statistical Inference

P-value = ?

Formal definition:

P-value = probability of observing a value more extreme than actual value observed, if the null hypothesis is true.

Simple definition:

P-value = Probability of Type 1 error, if the null hypothesis is true.

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Foundations of Statistical Inference

If P-value < alpha = ?

Decision Rule

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Foundations of Statistical Inference

If P-value > alpha = ?

Decision Rule

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Foundations of Statistical Inference

If we “fail to reject” (accept) Ho, we attribute any observed difference to ?

If we “fail to reject” (accept) Ho, we attribute any observed difference to sampling error only.

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Foundations of Statistical Inference

If 95% CI of “mean difference” includes zero = ?

Non-significant because includes 0.

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Foundations of Statistical Inference

What should you know about one vs. two-tailed tests?

One-tailed test for directional hypothesis
Two-tailed test for nondirectional hypothesis
Two-tailed test allows for possibility that difference may be positive or negative.
One-tailed test more powerful
More power = more likely to find significance when there is significance.
Less likely to commit Type II error

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# Foundations of Statistical Inference The probability of finding a statistically significant difference if such a difference exists in the real world = **?**

**Statistical Power** = The probability of finding a statistically significant difference if such a difference exists in the real world * The probability that the test correctly rejects the null hypothesis * Only matters when the null is false

# Foundations of Statistical Inference The Four Pillars of Power?

# Foundations of Statistical Inference How to manipulate the four pillars to increase power?

# Foundations of Statistical Inference How to manipulate the four pillars to decrease power?

# Foundations of Statistical Inference Determinants of Statistical Power?

**P** = power (1 – β) **A** = alpha level of significance **N** = sample size **E** = effect size * Knowing three of these four will allow for determination of the fourth.

# Foundations of Statistical Inference A priori = **?** ## Footnote Power Analysis

**A priori** = before data collection * Minimum sample required

# Foundations of Statistical Inference Post hoc = ? ## Footnote Power Analysis

**Post hoc** = after data collection * Only an issue if you fail to reject the null hypothesis

# Foundations of Statistical Inference Power with MCID and CI.

# Type I and Type II Errors A physical therapist conducts a study on the relationship between age and flexibility of the hamstrings. * *What is the null hypothesis*? * *Write a directional alternative hypothesis for this scenario*.

A physical therapist conducts a study on the relationship between age and flexibility of the hamstrings. * *What is the null hypothesis*? = **There is no correlation between age and hamstring flexibility.** * *Write a directional alternative hypothesis for this scenario*. = **There is a significant negative correlation between age and hamstring flexibility.**

# Type I and Type II Errors The physical therapist gathers data, and the data suggest there is no correlation between age and hamstring flexibility, when there truly is a negative correlation. * *Is the researcher correct or is this an error? If an error, what type*? * *If this is an error, what could the researcher do to mitigate this error*?

The physical therapist gathers data, and the data suggest there is no correlation between age and hamstring flexibility, when there truly is a negative correlation. * *Is the researcher correct or is this an error? If an error, what type*? = **This is a Type II error. “Failure to reject a FALSE null.”** * *If this is an error, what could the researcher do to mitigate this error*? = **This may be an issue of power. Two options are to increase the sample size or to increase alpha. Increasing alpha will decrease beta, which will increase power (1 – B). Increasing sample size is the better option.**

# Type I and Type II Errors A physical therapist conducts a study on the relationship between age and flexibility of the hamstrings. * *What is the null hypothesis*? = * *Write a nondirectional alternative hypothesis*? =

A physical therapist conducts a study on the relationship between age and flexibility of the hamstrings. * *What is the null hypothesis*? = **There is no correlation between age and hamstring flexibility.** * *Write a nondirectional alternative hypothesis*? = **There is a significant correlation between age and hamstring flexibility.**

# Type I and Type II Errors The physical therapist gathers data, and the data suggest there is a negative correlation between age and hamstring flexibility, when there truly is a negative correlation. * *Is the researcher correct or is this an error? If an error, what type?* * *If this is an error, what could the researcher do to mitigate this error*?

The physical therapist gathers data, and the data suggest there is a negative correlation between age and hamstring flexibility, when there truly is a negative correlation. * *Is the researcher correct or is this an error? If an error, what type?* = **The researcher is correct. ** * *If this is an error, what could the researcher do to mitigate this error*? = **N/A**

# Review of Experimental Designs True experimental or Quasi-experimental design?

True experimental design.

# Review of Experimental Designs What Design?

**Pretest-Posttest Control Group Design**: * Both groups are measured before and after treatment * Differences between the groups can be attributed to the treatment * Cause and effect (AKA, causation, causal relationship)

# Review of Experimental Designs

**Designs for Repeated Measures**: * Same people in each level of the IV = “within-subject design” * Single factor (one-way) repeated measures design * There is no control group – subjects act as their own controls

# Review of Experimental Designs Time can be the IV in a ?

Time can be the IV in a **single-factor repeated measures design**.

# Comparing Two Means Assumptions of Parametric Tests = __?__

1. **Scale data** (ratio or interval) - Calculate means and variance, so data should be continuous 2. **Random Sampling** - Though this is rare in PT research 3. **Equal Variance** - Used when there is more than one group. T-test, ANOVA. Groups were “roughly equivalent” before starting. Can be tested statistically 4. **Normality** - Data are sampled from a population with a normal distribution. Can be tested statistically

# Comparing Two Means Independent groups or Repeated measures?

# Comparing Two Means If t > 1, you have = ? If t < 1, you have = ?

* If t > 1, you have a greater difference between groups * If t < 1, you have more variability within groups

# Comparing Two Means The number of independent pieces of information that went into calculating the estimate = __?__

**Degrees of freedom** = The number of independent pieces of information that went into calculating the estimate.

# Comparing Two Means What kind of T-Test for independent groups?

# Comparing Two Means Independent (unpaired) t-test protocol?

# Comparing Two Means Assumptions for Unpaired t-Tests?

# Comparing Two Means Cohen’s d = **?**

# Comparing Two Means What kind of T-Test for repeated measures?

# Comparing Two Means Paired t-test protocol?

# Comparing Two Means Assumptions for Paired t-Tests

# t-Test Concepts A test for equal variances for independent groups t-test (and ANOVA) = __?__

**Levene’s Test**: A test for equal variances for independent groups t-test (and ANOVA) **Tests the null hypothesis**: * There is no significant difference in variance between groups the same p-value rules apply. * p < .05 we REJECT the null hypothesis = i.e. variances are NOT equal * p > .05 we ACCEPT (fail to reject) the null hypothesis i.e. variances ARE equal

# t-Test Concepts Conceptual basis of comparing means: independent groups?

# t-Test Concepts Conceptual basis of comparing means: repeated measures?

# ANOVA Concepts Basics of analysis of variance (ANOVA)?

# ANOVA Concepts Types of ANOVAs

# ANOVA Concepts Power and effect size (for ANOVA).

# ANOVA Concepts Multiple comparison tests for independent groups?

# ANOVA Concepts Multiple comparison tests for repeated measures?

Exam 1 Flashcards

(60 cards)