Movement Science Research Methods and Statistics Review

Comprehensive practice flashcards covering research methodology, study designs, research ethics, descriptive and inferential statistics, variability, z-scores, normal distributions, sampling distributions, hypothesis testing, and effect sizes.

What is the formal definition of research according to the lecture notes?

Research is the systematic investigation into and study of materials and sources in order to establish facts and reach new conclusions.

What are the five key characteristics of research?

1. Systematic (thorough and thoughtful design), 2. Logical (stems naturally from past research/theory), 3. Empirical (uses data to draw conclusions), 4. Reductive (takes a representative sample as reflective of general trends), 5. Replicable (fully and clearly outlines all procedures).

How does basic research differ from applied research?

Basic research is motivated by the discovery of new, highly specified knowledge (exploring chemical or cellular mechanisms in cell cultures or animal models), whereas applied research extends theories and knowledge into clinically relevant human samples with direct relevance to clinical outcomes.

What is the primary difference between quantitative research and qualitative research?

Quantitative research involves numerical data collection and focuses on the analysis of objective numerical independent and dependent variables, while qualitative research involves collecting non-numerical data and analyzing objective non-numerical outcomes.

What distinguishes original research from a review article?

Original research uses specific procedures in a sample to collect data, perform statistical analysis, and test a research question, whereas a review synthesizes, evaluates, and interprets results across a body of existing literature (sometimes using meta-analysis).

What are the seven steps of the scientific process in order?

1. Understand the research topic, 2. Identify your specific research question (specify independent and dependent variables), 3. Form hypotheses, 4. Design/plan methodology, 5. Collect data, 6. Analyze the data, 7. Interpret results and draw conclusions.

What are non-empirical publications in research literature?

Non-empirical publications include expert opinion, anecdotal evidence, and letters to the editor, which do not rely on systematic data collection.

What are case studies and case series, and what is their primary limitation?

They describe unique cases (or follow a collection of cases over time) in a very comprehensive manner, but their main limitation is that they lack a comparison or control group.

What are the key characteristics of a cross-sectional study?

Cross-sectional studies describe outcomes across a group of people, typically at just one time point. They offer better generalizability but less specificity, and may sometimes include a control group.

What is the primary goal and structure of a case-controlled study?

A case-controlled study compares an experimental case group to a matched control group that differs in only one key area (e.g., exposure or intervention), allowing estimation of treatment effects without a longitudinal design.

What are the main advantages and challenges of cohort studies?

Cohort studies are longitudinal studies that follow one or more groups over time to explore long-term effects or risk factors for injury/disease. They are very thorough, but participant retention can be a major roadblock.

How is a Randomized Controlled Trial (RCT) designed and what does it assess?

Participants from the same population are randomly assigned to a treatment group or control group and evaluated over time. RCTs effectively assess treatment efficacy and placebo effects while minimizing bias.

According to the evidence pyramid shown in the figure, which study design provides the highest quality of evidence among filtered information?

Systematic Reviews represent the top tier of filtered information and provide the highest quality of evidence on the pyramid.

How do experimental and non-experimental research designs differ in establishing causation?

Experimental research determines cause and effect by manipulating the independent variable and controlling extraneous variables. Non-experimental research infers causation by systematically recruiting participants based on the independent variable while controlling extraneous variables.

What ethical obligations must researchers fulfill before a participant joins a study?

Researchers must obtain informed consent, outline foreseeable risks and benefits, explain privacy and confidentiality protections, and reassure participants that they can withdraw at any time without penalty.

What basic rights do research participants possess?

Participants have the right to privacy or nonparticipation, anonymity, confidentiality, and responsible conduct from the experimenter.

What required elements must be included in an informed consent document?

An invitation to participate, explanation of procedures, description of risks/discomforts, expected benefits, confidentiality maintenance procedures, contact information for study inquiries, and an explicit statement that participation is voluntary and withdrawal is allowed at any time.

What constitutes scientific misconduct in research?

Scientific misconduct is defined as fabrication, falsification, or plagiarism in proposing, performing, reviewing, or reporting research results.

What is peer review, and what three decisions can reviewers recommend?

Peer review is an evaluation of research by $2$ to $4$ independent scientists who can recommend acceptance, revision (the most common result), or rejection.

What are the standard sections of a published original research article in order?

Title, Author information, Abstract, Introduction, Method and Materials, Results, Discussion, Conclusion, Acknowledgements, and References.

What five key aspects should be evaluated when reading the Methods section of a study?

The who, where, when, what, and how of the study methodology.

What is the difference between a parameter and a statistic?

A parameter is a characteristic of an entire population, whereas a statistic is a characteristic of a sample used to estimate the population parameter.

How is sampling error defined?

Sampling error is the naturally occurring discrepancy or error that exists between a sample statistic and the corresponding population parameter.

What is the difference between descriptive statistics and inferential statistics?

Descriptive statistics summarize, organize, and simplify sample data, whereas inferential statistics make generalizations or statements about populations based on sample data.

What is the difference between an independent variable and a dependent variable?

An independent variable is controlled or selected by the researcher (e.g., year in school), while a dependent variable is the outcome measure being evaluated (e.g., GPA).

What are the four scales of measurement in statistics?

Nominal, Ordinal, Interval, and Ratio scales.

What are the properties and an example of a nominal scale?

A nominal scale consists of mutually exclusive categories without quantitative differentiation or order (e.g., hair color).

What are the properties and an example of an ordinal scale?

An ordinal scale has quantitative order (magnitude), but equal distances between scores are not implied (e.g., a pain scale).

What are the properties and an example of an interval scale?

An interval scale has ordered categories with equal intervals of magnitude between numbers, but no absolute/meaningful zero point (e.g., temperature in Celsius or Fahrenheit).

What are the properties and an example of a ratio scale?

A ratio scale has ordered categories, equal intervals, and a meaningful absolute zero point representing the absence of the property (e.g., distance, where $2\,miles$ is twice as long as $1\,mile$).

What are five common graphical methods used to display data?

1. Histograms (distribution of values), 2. Bar graphs (comparing groups/conditions), 3. Scatter plots (visualizing relationships/trends), 4. Pie charts (relative proportions), 5. Time series graphs (trends over time).

In a frequency distribution table, what do the column headers 'f', 'Prop', 'Perc', 'cf', and 'c%' represent?

'f' is frequency, 'Prop' is proportion ($\frac{f}{N}$), 'Perc' is percentage ($\frac{f}{N} \times 100$), 'cf' is cumulative frequency, and 'c%' is cumulative percentage.

Based on the frequency distribution table shown in the figure, what is the cumulative percentage ($c\%$) for a score of $X = 4$?

The cumulative percentage ($c\%$) for $X = 4$ is $93\%$ (corresponding to the 93rd percentile).

What is the definition of a percentile?

A percentile is the rank of a particular score representing the percentage of individuals in the distribution with scores at or below that value.

What three primary characteristics are used to describe any distribution of scores?

1. Shape, 2. Central tendency, 3. Variability.

What are the defining properties of a normal distribution?

A normal distribution (Gaussian curve) is bell-shaped, symmetrical, and represents the natural distribution of most population-level continuous variables.

Based on the figure showing kurtosis curves, what are the names and descriptions of curves (a), (b), and (c)?

(a) Mesokurtic curve (normal bell-shape), (b) Platykurtic curve (flat, wide distribution), and (c) Leptokurtic curve (tall, skinny peak with steep tail drop).

What is a skewed distribution?

A distribution where scores accumulate on one end of the scale and taper off gradually at the other end.

What are the three common measures of central tendency?

Mean (arithmetic average), Median (50th percentile midpoint), and Mode (most frequent score).

Under what conditions is the mean the best measure of central tendency?

When data are on interval or ratio scales and the distribution is symmetrical/normal without extreme outliers.

When should the median be used instead of the mean?

The median should be used when dealing with ordinal data, skewed distributions, extreme scores (outliers), undetermined values, or open-ended distributions.

When is the mode the preferred measure of central tendency?

The mode is best for nominal scale data or discrete variables where averaging is non-sensical (e.g., modal number of children per family).

What are the main statistical measures of variability?

Range, interquartile range (IQR), deviation scores, sum of squares ($SS$), variance ($\sigma^2$ or $s^2$), and standard deviation ($\sigma$ or $s$).

How is the interquartile range (IQR) calculated and what is its advantage over range?

IQR is the difference between raw scores at the 75th and 25th percentiles. Unlike range, IQR is not affected by extreme outliers.

What is a deviation score in statistics?

A deviation score is the distance between an individual score and the mean for that variable, calculated as $X - \mu$ (or $X - \bar{X}$).

What is the formula for the population Sum of Squares ($SS$)?

$$SS = \sum (X - \mu)^2$$

What is the formula for population variance ($\sigma^2$)?

$$\sigma^2 = \frac{SS}{N} = \frac{\sum (X - \mu)^2}{N}$$

What is the formula for population standard deviation ($\sigma$)?

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{\sum (X - \mu)^2}{N}}$$

Why is sample variance calculated by dividing by degrees of freedom ($df = n - 1$) instead of $n$?

Because sample variability underestimates population variability due to sampling error; dividing by $n - 1$ provides an unbiased estimate of the population variance.

What is the formula for sample variance ($s^2$) shown in the provided figure?

$$s^2 = \frac{SS}{n - 1} = \frac{\sum (X - \bar{X})^2}{n - 1}$$

What is the formula for sample standard deviation ($s$)?

$$s = \sqrt{s^2} = \sqrt{\frac{\sum (X - \bar{X})^2}{n - 1}}$$

How do low vs. high standard deviation values affect the distribution curve?

Low SD values mean data points are tightly packed around the mean (narrow distribution), while high SD values mean data points are spread farther from the mean (wider distribution).

What happens to the standard deviation of a dataset if you add a constant to every score, versus multiplying every score by a constant?

Adding a constant to each score does not change the SD; multiplying each score by a constant multiplies the SD by that same constant.

What are the six steps to calculate the sample standard deviation ($s$) from raw scores?

1. Calculate sample mean ($\bar{X}$), 2. Compute individual deviations ($X - \bar{X}$), 3. Square each deviation, 4. Sum squared deviations to get $SS$, 5. Divide $SS$ by $n - 1$ to get sample variance ($s^2$), 6. Take the square root of $s^2$.

In a standard normal distribution curve, what percentage of scores fall within $\pm 1\sigma$, $\pm 2\sigma$, and $\pm 3\sigma$ of the mean?

Within $\pm 1\sigma$ is $68.2\%$ ($34.1\% + 34.1\%$), within $\pm 2\sigma$ is $95.4\%$ ($68.2\% + 13.6\% + 13.6\%$), and within $\pm 3\sigma$ is $99.6\%$ ($95.4\% + 2.1\% + 2.1\%$).

What is a z-score and what does its sign indicate?

A z-score expresses a raw score in standard deviation units relative to the mean. A positive sign ($+$) means the score is above the mean, while a negative sign ($-$) means it is below the mean.

What are the z-score formulas for a population versus a sample?

Population z-score: $z = \frac{X - \mu}{\sigma}$ ; Sample z-score: $z = \frac{X - \bar{X}}{s}$.

For a population of college males with mean weight $\mu = 175\,lbs$ and $\sigma = 25\,lbs$, what are the z-scores for students weighing $200\,lbs$ and $125\,lbs$?

For $200\,lbs$: $z = \frac{200 - 175}{25} = +1.0$. For $125\,lbs$: $z = \frac{125 - 175}{25} = -2.0$.

If kinesiology students have a mean grip strength of $\bar{X} = 34\,psi$ and $s = 6\,psi$, what is the z-score and area under the normal curve between the mean and $X = 41\,psi$?

z-score = $\frac{41 - 34}{6} = 1.17$. The area under the normal curve between the mean and $z = 1.17$ is $37.901\%$.

For a sample of 7 math majors guessing numbers with values $X = \{5, 3, 8, 7, 7, 4, 6\}$, what are the Mean, Median, and Mode?

Mean $\bar{X} = 5.71$, Median $= 6$, and Mode $= 7$.

For the sample dataset $X = \{5, 3, 8, 7, 7, 4, 6\}$ with mean $\bar{X} = 5.71$, what are the sample variance ($s^2$) and sample standard deviation ($s$)?

Sum of squares $SS = 19.43$, Sample variance $s^2 = \frac{19.43}{7 - 1} = 3.24$, and Sample SD $s = \sqrt{3.24} = 1.80$.

For a student who guessed $X = 5$ in a dataset with $\bar{X} = 5.71$ and $s = 1.80$, what is the z-score and corresponding percentile?

z-score $z = \frac{5 - 5.71}{1.80} = -0.39$. Area between mean and $z$ is $15.172\%$. Percentile $= 50\% - 15.172\% = 34.828\%$.

In the dataset with $\bar{X} = 5.71$ and $s = 1.80$, what percentage of people guessed between $4$ and $7$?

For $X_1 = 4$: $z_1 = \frac{4 - 5.71}{1.80} = -0.95$ ($\text{AUC}_1 = 32.895\%$). For $X_2 = 7$: $z_2 = \frac{7 - 5.71}{1.80} = 0.72$ ($\text{AUC}_2 = 26.423\%$). Total percentage $= 32.895\% + 26.423\% = 59.318\%$.

In a distribution with $\bar{X} = 5.71$ and $s = 1.80$, what raw score $X$ corresponds to the 30th percentile?

30th percentile leaves $20\%$ area between mean and $z$, so $z = -0.53$. Solving $-0.53 = \frac{X - 5.71}{1.80}$ gives $X = 5.71 - 0.954 = 4.756$.

What is the distribution of sample means (sampling distribution)?

It is the collection of sample means for all possible random samples of a specific sample size ($n$) drawn from a population.

What are the three key assertions of the Central Limit Theorem (CLT)?

For any population with mean $\mu$ and standard deviation $\sigma$, as $n \rightarrow \infty$ (typically $n > 30$): 1. The distribution of sample means has mean $\mu$, 2. Its SD is $\frac{\sigma}{\sqrt{n}}$, 3. The shape approaches a normal distribution regardless of population shape.

What is the Standard Error of the Mean ($SE_M$) and its formulas?

$SE_M$ is the standard deviation of the sampling distribution of sample means. Formula when $\sigma$ is known: $SE_M = \frac{\sigma}{\sqrt{n}}$; when $s$ is estimated: $SE_M = \frac{s}{\sqrt{n}}$.

What are the four steps of hypothesis testing?

1. State the statistical hypotheses ($H_0$ and $H_1$), 2. Set criteria for decision (alpha level, 1- or 2-tailed), 3. Collect data and compute sample statistics ($z_{observed}$), 4. Make a statistical decision ($z_{observed}$ vs $z_{critical}$).

How are the null hypothesis ($H_0$) and alternative hypothesis ($H_1$) defined?

Null hypothesis ($H_0$) states there is no effect, no difference, or no correlation. Alternative hypothesis ($H_1$) states there is a real effect, difference, or correlation. They are mutually exclusive.

What is the significance level (alpha level, $\alpha$)?

Alpha level is the probability threshold used to define sample outcome values that are 'very unlikely' if the null hypothesis is true, commonly set at $\alpha = 0.05$, $0.01$, or $0.001$.

What are the two-tailed critical z-values ($z_{critical}$) for $\alpha = 0.05$, $\alpha = 0.01$, and $\alpha = 0.001$?

For $\alpha = 0.05$: $z_{critical} = \pm 1.96$ ; for $\alpha = 0.01$: $z_{critical} = \pm 2.58$ ; for $\alpha = 0.001$: $z_{critical} = \pm 3.30$.

What decision matrix defines Type I and Type II errors?

Rejecting $H_0$ when $H_0$ is true is a Type I Error. Failing to reject $H_0$ when $H_0$ is false is a Type II Error. Correct decisions occur when rejecting false $H_0$ or failing to reject true $H_0$.

How do mean difference, variability, and sample size impact the calculated $z_{observed}$ value in hypothesis testing?

1. Larger mean difference increases $z_{observed}$ (more likely to reject $H_0$), 2. Higher variability increases $SE_M$, decreasing $z_{observed}$ (less likely to reject $H_0$), 3. Larger sample size ($n$) decreases $SE_M$, increasing $z_{observed}$ (more likely to reject $H_0$).

In a hypothesis test where a sample of 7 math majors has $\bar{X} = 5.71$, tested against general population $\mu = 6.7$ with $s = 1.2$, what is $z_{observed}$ and the statistical conclusion at $\alpha = 0.05$?

$SE_M = \frac{1.2}{\sqrt{7}} = 0.45$. $z_{observed} = \frac{5.71 - 6.7}{0.45} = -2.20$. Since $|-2.20| > 1.96$ ($z_{critical}$), we reject $H_0$ and conclude math majors guess significantly different numbers than the general population.

What is Cohen's d, its formula, and the standards for small, medium, and large effect sizes?

Cohen's d measures treatment effect magnitude independent of sample size: $d = \frac{\mu_{Treatment} - \mu_{Control}}{\sigma}$. Effect size standards: Small ($d = 0.2 - 0.5$), Medium ($d = 0.5 - 0.8$), Large ($d \ge 0.8$).